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{{task}}
The factorial of a number, written as , is defined as .
[http://mathworld.wolfram.com/Multifactorial.html Multifactorials] generalize factorials as follows: : : : : :
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
'''Note:''' The [[wp:Factorial#Multifactorials|wikipedia entry on multifactorials]] gives a different formula. This task uses the [http://mathworld.wolfram.com/Multifactorial.html Wolfram mathworld definition].
360 Assembly
For maximum compatibility, this program uses only the basic instruction set (S/360 1964 POP).
* Multifactorial 09/05/2016
MULFACR CSECT
USING MULFACR,13
SAVEAR B STM-SAVEAR(15)
DC 17F'0'
STM STM 14,12,12(13) prolog
ST 13,4(15) "
ST 15,8(13) "
LR 13,15 "
LA I,1 i=1
LOOPI C I,D do i=1 to deg
BH ELOOPI leave i
LA L,W+4 l=@p
LA J,1 j=1
LOOPJ C J,N do j=1 to num
BH ELOOPJ leave j
LA R,1 r=1
LCR S,I s=-i
LR K,J k=j
LOOPK C K,=F'2' do k=j to 2 by s
BL ELOOPK leave k
MR RR,K r=r*k
AR K,S k=k+s
B LOOPK next k
ELOOPK CVD R,Y pack r
MVC X,=XL12'402020202020202020202120' ed mask
ED X,Y+2 edit r
MVC 0(8,L),X+4 output r
LA L,8(L) l=l+8
LA J,1(J) j=j+1
B LOOPJ next j
ELOOPJ WTO MF=(E,W)
LA I,1(I) i=i+1
B LOOPI next i
ELOOPI L 13,4(0,13) epilog
LM 14,12,12(13) "
XR 15,15 "
BR 14 "
N DC F'10' number
D DC F'5' degree
W DC 0F,H'84',H'0',CL80' ' length,zero,text
X DS CL12 temp
Y DS D packed PL8
I EQU 6
J EQU 7
K EQU 8
S EQU 9
RR EQU 10 even reg of R for MR opcode
R EQU 11
L EQU 12
END MULFACR
{{out}}
1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50
Ada
with Ada.Text_IO; use Ada.Text_IO;
procedure Mfact is
function MultiFact (num : Natural; deg : Positive) return Natural is
Result, N : Integer := num;
begin
if N = 0 then return 1; end if;
loop
N := N - deg; exit when N <= 0; Result := Result * N;
end loop; return Result;
end MultiFact;
begin
for deg in 1..5 loop
Put("Degree"& Integer'Image(deg) &":");
for num in 1..10 loop Put(Integer'Image(MultiFact(num,deg))); end loop;
New_line;
end loop;
end Mfact;
{{out}}
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
Aime
mf(integer a, n)
{
integer o;
o = 1;
do {
o *= a;
} while (0 < (a -= n));
o;
}
main(void)
{
integer i, j;
i = 0;
while ((i += 1) <= 5) {
o_("degree ", i, ":");
j = 0;
while ((j += 1) <= 10) {
o_("\t", mf(j, i));
}
o_("\n");
}
0;
}
{{out}}
degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
degree 2: 1 2 3 8 15 48 105 384 945 3840
degree 3: 1 2 3 4 10 18 28 80 162 280
degree 4: 1 2 3 4 5 12 21 32 45 120
degree 5: 1 2 3 4 5 6 14 24 36 50
ALGOL 68
Translation of C.
BEGIN
INT highest degree = 5;
INT largest number = 10;
CO Recursive implementation of multifactorial function CO
PROC multi fact = (INT n, deg) INT :
(n <= deg | n | n * multi fact(n - deg, deg));
CO Iterative implementation of multifactorial function CO
PROC multi fact i = (INT n, deg) INT :
BEGIN
INT result := n, nn := n;
WHILE (nn >= deg + 1) DO
result TIMESAB nn - deg;
nn MINUSAB deg
OD;
result
END;
CO Print out multifactorials CO
FOR i TO highest degree DO
printf (($l, "Degree ", g(0), ":"$, i));
FOR j TO largest number DO
printf (($xg(0)$, multi fact (j, i)))
OD
OD
END
{{out}}
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
ALGOL W
Iterative multifactorial based on Ada, AutoHotkey, etc.
begin
% returns the multifactorial of n with the specified degree %
integer procedure multifactorial ( integer value n, degree ) ;
begin
integer mf, v;
mf := v := n;
while begin
v := v - degree;
v > 1
end do mf := mf * v;
mf
end multifactorial ;
% tests as per task %
for degree := 1 until 5 do begin
i_w := 1; s_w := 0; % output formatting %
write( "Degree: ", degree, ":" );
for v := 1 until 10 do begin
writeon( " ", multifactorial( v, degree ) )
end for_v
end for_degree
end.
{{out}}
Degree: 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree: 2: 1 2 3 8 15 48 105 384 945 3840
Degree: 3: 1 2 3 4 10 18 28 80 162 280
Degree: 4: 1 2 3 4 5 12 21 32 45 120
Degree: 5: 1 2 3 4 5 6 14 24 36 50
ANSI Standard BASIC
Translation of FreeBASIC.
100 FUNCTION multiFactorial (n, degree)
110 IF n < 2 THEN
120 LET multiFactorial = 1
130 EXIT FUNCTION
140 END IF
150 LET result = n
160 FOR i = n - degree TO 2 STEP -degree
170 LET result = result * i
180 NEXT i
190 LET multiFactorial = result
200 END FUNCTION
210
220 FOR degree = 1 TO 5
230 PRINT "Degree"; degree; " => ";
240 FOR n = 1 TO 10
250 PRINT multiFactorial(n, degree); " ";
260 NEXT n
270 PRINT
280 NEXT degree
290 END
AutoHotkey
Loop, 5 {
Output .= "Degree " (i := A_Index) ": "
Loop, 10
Output .= MultiFact(A_Index, i) (A_Index = 10 ? "`n" : ", ")
}
MsgBox, % Output
MultiFact(n, d) {
Result := n
while 1 < n -= d
Result *= n
return, Result
}
'''Output:'''
Degree 1: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800
Degree 2: 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840
Degree 3: 1, 2, 3, 4, 10, 18, 28, 80, 162, 280
Degree 4: 1, 2, 3, 4, 5, 12, 21, 32, 45, 120
Degree 5: 1, 2, 3, 4, 5, 6, 14, 24, 36, 50
AWK
# syntax: GAWK -f MULTIFACTORIAL.AWK
# converted from Go
BEGIN {
for (k=1; k<=5; k++) {
printf("degree %d:",k)
for (n=1; n<=10; n++) {
printf(" %d",multi_factorial(n,k))
}
printf("\n")
}
exit(0)
}
function multi_factorial(n,k, r) {
r = 1
for (; n>1; n-=k) {
r *= n
}
return(r)
}
{{out}}
degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
degree 2: 1 2 3 8 15 48 105 384 945 3840
degree 3: 1 2 3 4 10 18 28 80 162 280
degree 4: 1 2 3 4 5 12 21 32 45 120
degree 5: 1 2 3 4 5 6 14 24 36 50
BBC BASIC
multifact
FOR i% = 1 TO 5
PRINT "Degree "; i%; ":";
FOR j% = 1 TO 10
PRINT " ";FNmultifact(j%, i%);
NEXT
PRINT
NEXT
END
:
DEF FNmultifact(n%, degree%)
LOCAL i%, mfact%
mfact% = 1
FOR i% = n% TO 1 STEP -degree%
mfact% = mfact% * i%
NEXT
= mfact%
{{out}}
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
C
{{uses from|Library|C Runtime|component1=printf}}
/* Include statements and constant definitions */ #include <stdio.h> #define HIGHEST_DEGREE 5 #define LARGEST_NUMBER 10 /* Recursive implementation of multifactorial function */ int multifact(int n, int deg){ return n <= deg ? n : n * multifact(n - deg, deg); } /* Iterative implementation of multifactorial function */ int multifact_i(int n, int deg){ int result = n; while (n >= deg + 1){ result *= (n - deg); n -= deg; } return result; } /* Test function to print out multifactorials */ int main(void){ int i, j; for (i = 1; i <= HIGHEST_DEGREE; i++){ printf("\nDegree %d: ", i); for (j = 1; j <= LARGEST_NUMBER; j++){ printf("%d ", multifact(j, i)); } } }
{{out}}
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
C#
namespace RosettaCode.Multifactorial { using System; using System.Linq; internal static class Program { private static void Main() { Console.WriteLine(string.Join(Environment.NewLine, Enumerable.Range(1, 5) .Select( degree => string.Join(" ", Enumerable.Range(1, 10) .Select( number => Multifactorial(number, degree)))))); } private static int Multifactorial(int number, int degree) { if (degree < 1) { throw new ArgumentOutOfRangeException("degree"); } var count = 1 + (number - 1) / degree; if (count < 1) { throw new ArgumentOutOfRangeException("number"); } return Enumerable.Range(0, count) .Aggregate(1, (accumulator, index) => accumulator * (number - degree * index)); } } }
Output:
1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50
C++
#include <algorithm> #include <iostream> #include <iterator> /*Generate multifactorials to 9 Nigel_Galloway November 14th., 2012. */ int main(void) { for (int g = 1; g < 10; g++) { int v[11], n=0; generate_n(std::ostream_iterator<int>(std::cout, " "), 10, [&]{n++; return v[n]=(g<n)? v[n-g]*n : n;}); std::cout << std::endl; } return 0; }
{{out}}
1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50
1 2 3 4 5 6 7 16 27 40
1 2 3 4 5 6 7 8 18 30
1 2 3 4 5 6 7 8 9 20
1 2 3 4 5 6 7 8 9 10
Clojure
(defn !! [m n] (->> (iterate #(- % m) n) (take-while pos?) (apply *))) (doseq [m (range 1 6)] (prn m (map #(!! m %) (range 1 11))))
{{out}}
1 (1 2 6 24 120 720 5040 40320 362880 3628800)
2 (1 2 3 8 15 48 105 384 945 3840)
3 (1 2 3 4 10 18 28 80 162 280)
4 (1 2 3 4 5 12 21 32 45 120)
5 (1 2 3 4 5 6 14 24 36 50)
Common Lisp
(defun mfac (n m) (reduce #'* (loop for i from n downto 1 by m collect i))) (loop for i from 1 to 10 do (format t "~2@a: ~{~a~^ ~}~%" i (loop for j from 1 to 10 collect (mfac j i))))
{{out}}
1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50
6: 1 2 3 4 5 6 7 16 27 40
7: 1 2 3 4 5 6 7 8 18 30
8: 1 2 3 4 5 6 7 8 9 20
9: 1 2 3 4 5 6 7 8 9 10
10: 1 2 3 4 5 6 7 8 9 10
D
import std.stdio, std.algorithm, std.range; T multifactorial(T=long)(in int n, in int m) pure /*nothrow*/ { T one = 1; return reduce!q{a * b}(one, iota(n, 0, -m)); } void main() { foreach (immutable m; 1 .. 11) writefln("%2d: %s", m, iota(1, 11) .map!(n => multifactorial(n, m))); }
{{out}}
1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50
6: 1 2 3 4 5 6 7 16 27 40
7: 1 2 3 4 5 6 7 8 18 30
8: 1 2 3 4 5 6 7 8 9 20
9: 1 2 3 4 5 6 7 8 9 10
10: 1 2 3 4 5 6 7 8 9 10
Dart
main() { int n=5,d=3; int z= fact(n,d); print('$n factorial of degree $d is $z'); for(var j=1;j<=5;j++) { print('first 10 numbers of degree $j :'); for(var i=1;i<=10;i++) { int z=fact(i,j); print('$z'); } print('\n'); } } int fact(int a,int b) { if(a<=b||a==0) return a; if(a>1) return a*fact((a-b),b); }
Elixir
{{trans|Erlang}}
defmodule RC do def multifactorial(n,d) do Enum.take_every(n..1, d) |> Enum.reduce(1, fn x,p -> x*p end) end end Enum.each(1..5, fn d -> multifac = for n <- 1..10, do: RC.multifactorial(n,d) IO.puts "Degree #{d}: #{inspect multifac}" end)
{{out}}
Degree 1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
Degree 2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
Degree 3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
Degree 4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
Degree 5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
Erlang
-module(multifac). -compile(export_all). multifac(N,D) -> lists:foldl(fun (X,P) -> X * P end, 1, lists:seq(N,1,-D)). main() -> Ds = lists:seq(1,5), Ns = lists:seq(1,10), lists:foreach(fun (D) -> io:format("Degree ~b: ~p~n",[D, [ multifac(N,D) || N <- Ns]]) end, Ds).
{{out}}
multifac:main().
Degree 1: [1,2,6,24,120,720,5040,40320,362880,3628800]
Degree 2: [1,2,3,8,15,48,105,384,945,3840]
Degree 3: [1,2,3,4,10,18,28,80,162,280]
Degree 4: [1,2,3,4,5,12,21,32,45,120]
Degree 5: [1,2,3,4,5,6,14,24,36,50]
ok
ERRE
PROGRAM MULTIFACTORIAL
PROCEDURE MULTI_FACT(NUM,DEG->MF)
RESULT=NUM
N=NUM
IF N=0 THEN
MF=1
EXIT PROCEDURE
END IF
LOOP
N-=DEG
EXIT IF N<=0
RESULT*=N
END LOOP
MF=RESULT
END PROCEDURE
BEGIN
PRINT(CHR$(12);)
FOR DEG=1 TO 10 DO
PRINT("Degree";DEG;":";)
FOR NUM=1 TO 10 DO
MULTI_FACT(NUM,DEG->MF)
PRINT(MF;)
END FOR
PRINT
END FOR
END PROGRAM
Degree 1 : 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2 : 1 2 3 8 15 48 105 384 945 3840
Degree 3 : 1 2 3 4 10 18 28 80 162 280
Degree 4 : 1 2 3 4 5 12 21 32 45 120
Degree 5 : 1 2 3 4 5 6 14 24 36 50
Degree 6 : 1 2 3 4 5 6 7 16 27 40
Degree 7 : 1 2 3 4 5 6 7 8 18 30
Degree 8 : 1 2 3 4 5 6 7 8 9 20
Degree 9 : 1 2 3 4 5 6 7 8 9 10
Degree 10 : 1 2 3 4 5 6 7 8 9 10
=={{header|F_Sharp|F#}}==
let rec mfact d = function | n when n <= d -> n | n -> n * mfact d (n-d) [<EntryPoint>] let main argv = let (|UInt|_|) = System.UInt32.TryParse >> function | true, v -> Some v | false, _ -> None let (maxDegree, maxN) = match argv with | [| UInt d; UInt n |] -> (int d, int n) | [| UInt d |] -> (int d, 10) | _ -> (5, 10) let showFor d = List.init maxN (fun i -> mfact d (i+1)) |> printfn "%i: %A" d ignore (List.init maxDegree (fun i -> showFor (i+1))) 0
1: [1; 2; 6; 24; 120; 720; 5040; 40320; 362880; 3628800]
2: [1; 2; 3; 8; 15; 48; 105; 384; 945; 3840]
3: [1; 2; 3; 4; 10; 18; 28; 80; 162; 280]
4: [1; 2; 3; 4; 5; 12; 21; 32; 45; 120]
5: [1; 2; 3; 4; 5; 6; 14; 24; 36; 50]
Factor
: multifactorial ( n degree -- m )
neg 1 swap
: mf-row ( degree -- ) dup "Degree %d: " printf 10 [1,b] [ swap multifactorial pprint bl ] with each ;
: main ( -- ) 5 [1,b] [ mf-row nl ] each ;
MAIN: main
{{out}}
```txt
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
Forth
{{out}}
```txt
test
1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50
ok
Fortran
{{works with|Fortran|95 and later}}
program test
implicit none
integer :: i, j, n
do i = 1, 5
write(*, "(a, i0, a)", advance = "no") "Degree ", i, ": "
do j = 1, 10
n = multifactorial(j, i)
write(*, "(i0, 1x)", advance = "no") n
end do
write(*,*)
end do
contains
function multifactorial (range, degree)
integer :: multifactorial, range, degree
integer :: k
multifactorial = product((/(k, k=range, 1, -degree)/))
end function multifactorial
end program test
{{out}}
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
FreeBASIC
' FB 1.05.0 Win64
Function multiFactorial (n As UInteger, degree As Integer) As UInteger
If n < 2 Then Return 1
Var result = n
For i As Integer = n - degree To 2 Step -degree
result *= i
Next
Return result
End Function
For degree As Integer = 1 To 5
Print "Degree"; degree; " => ";
For n As Integer = 1 To 10
Print multiFactorial(n, degree); " ";
Next n
Print
Next degree
Print
Print "Press any key to quit"
Sleep
{{out}}
Degree 1 => 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2 => 1 2 3 8 15 48 105 384 945 3840
Degree 3 => 1 2 3 4 10 18 28 80 162 280
Degree 4 => 1 2 3 4 5 12 21 32 45 120
Degree 5 => 1 2 3 4 5 6 14 24 36 50
FunL
def multifactorial( n, d ) = product( n..1 by -d )
for d <- 1..5
println( d, [multifactorial(i, d) | i <- 1..10] ))
{{out}}
1, [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
2, [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
3, [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
4, [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
5, [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
GAP
MultiFactorial := function(n, k)
local r;
r := 1;
while n > 1 do
r := r*n;
n := n - k;
od;
return r;
end;
PrintArray(List([1 .. 10], n -> List([1 .. 5], k -> MultiFactorial(n, k))));
[ [ 1, 1, 1, 1, 1 ],
[ 2, 2, 2, 2, 2 ],
[ 6, 3, 3, 3, 3 ],
[ 24, 8, 4, 4, 4 ],
[ 120, 15, 10, 5, 5 ],
[ 720, 48, 18, 12, 6 ],
[ 5040, 105, 28, 21, 14 ],
[ 40320, 384, 80, 32, 24 ],
[ 362880, 945, 162, 45, 36 ],
[ 3628800, 3840, 280, 120, 50 ] ]
Go
package main import "fmt" func multiFactorial(n, k int) int { r := 1 for ; n > 1; n -= k { r *= n } return r } func main() { for k := 1; k <= 5; k++ { fmt.Print("degree ", k, ":") for n := 1; n <= 10; n++ { fmt.Print(" ", multiFactorial(n, k)) } fmt.Println() } }
{{out}}
degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
degree 2: 1 2 3 8 15 48 105 384 945 3840
degree 3: 1 2 3 4 10 18 28 80 162 280
degree 4: 1 2 3 4 5 12 21 32 45 120
degree 5: 1 2 3 4 5 6 14 24 36 50
Haskell
mulfac k = 1:s where s = [1 .. k] ++ zipWith (*) s [k+1..] -- for single n mulfac1 k n = product [n, n-k .. 1] main = mapM_ (print . take 10 . tail . mulfac) [1..5]
{{out}}
[1,2,6,24,120,720,5040,40320,362880,3628800]
[1,2,3,8,15,48,105,384,945,3840]
[1,2,3,4,10,18,28,80,162,280]
[1,2,3,4,5,12,21,32,45,120]
[1,2,3,4,5,6,14,24,36,50]
==Icon and {{header|Unicon}}==
The following is Unicon specific but can be readily translated into Icon:
procedure main(A)
l := integer(A[1]) | 10
every writeRow(n := !l, [: mf(!10,n) :])
end
procedure writeRow(n, r)
writes(right(n,3),": ")
every writes(right(!r,8)|"\n")
end
procedure mf(n, m)
if n <= 0 then return 1
return n*mf(n-m, m)
end
Sample run:
->mf 5
1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50
->
=={{header|IS-BASIC}}==
## J
```J
NB. tacit implementation of the recursive c function
NB. int multifact(int n,int deg){return n<=deg?n:n*multifact(n-deg,deg);}
multifact=: [`([ * - $: ])@.(<~)
(a:,<' degree'),multifact table >:i.10
┌─────────┬──────────────────────────────────────┐
│ │ degree │
├─────────┼──────────────────────────────────────┤
│multifact│ 1 2 3 4 5 6 7 8 9 10│
├─────────┼──────────────────────────────────────┤
│ 1 │ 1 1 1 1 1 1 1 1 1 1│
│ 2 │ 2 2 2 2 2 2 2 2 2 2│
│ 3 │ 6 3 3 3 3 3 3 3 3 3│
│ 4 │ 24 8 4 4 4 4 4 4 4 4│
│ 5 │ 120 15 10 5 5 5 5 5 5 5│
│ 6 │ 720 48 18 12 6 6 6 6 6 6│
│ 7 │ 5040 105 28 21 14 7 7 7 7 7│
│ 8 │ 40320 384 80 32 24 16 8 8 8 8│
│ 9 │ 362880 945 162 45 36 27 18 9 9 9│
│10 │3628800 3840 280 120 50 40 30 20 10 10│
└─────────┴──────────────────────────────────────┘
Java
public class MultiFact { private static long multiFact(long n, int deg){ long ans = 1; for(long i = n; i > 0; i -= deg){ ans *= i; } return ans; } public static void main(String[] args){ for(int deg = 1; deg <= 5; deg++){ System.out.print("degree " + deg + ":"); for(long n = 1; n <= 10; n++){ System.out.print(" " + multiFact(n, deg)); } System.out.println(); } } }
{{out}}
degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
degree 2: 1 2 3 8 15 48 105 384 945 3840
degree 3: 1 2 3 4 10 18 28 80 162 280
degree 4: 1 2 3 4 5 12 21 32 45 120
degree 5: 1 2 3 4 5 6 14 24 36 50
JavaScript
Iterative
{{trans|C}}
function multifact(n, deg){ var result = n; while (n >= deg + 1){ result *= (n - deg); n -= deg; } return result; }
function test (n, deg) { for (var i = 1; i <= deg; i ++) { var results = ''; for (var j = 1; j <= n; j ++) { results += multifact(j, i) + ' '; } console.log('Degree ' + i + ': ' + results); } }
{{out}}
test(10, 5) Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
Recursive
{{trans|C}}
function multifact(n, deg){ return n <= deg ? n : n * multifact(n - deg, deg); }
Test
function test (n, deg) { for (var i = 1; i <= deg; i ++) { var results = ''; for (var j = 1; j <= n; j ++) { results += multifact(j, i) + ' '; } console.log('Degree ' + i + ': ' + results); } }
{{Out}}
test(10, 5) Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 2 3 4 10 18 28 80 162 280 Degree 4: 1 2 3 4 5 12 21 32 45 120 Degree 5: 1 2 3 4 5 6 14 24 36 50
jq
{{works with|jq|1.4}}
# Input: n
# Output: n * (n - d) * (n - 2d) ...
def multifactorial(d):
. as $n
| ($n / d | floor) as $k
| reduce ($n - (d * range(0; $k))) as $i (1; . * $i);
# Print out a d-by-n table of multifactorials neatly:
def table(d; n):
def lpad(i): tostring | (i - length) * " " + .;
def pp(stream): reduce stream as $i (""; . + ($i | lpad(8)));
range(1; d+1) as $d | "Degree \($d): \( pp(range(1; n+1) | multifactorial($d)) )";
The specific task:
table(5; 10)
{{out}}
$ jq -n -r -f Multifactorial.jq Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 Degree 2: 1 2 3 8 15 48 105 384 945 3840 Degree 3: 1 1 3 4 5 18 28 40 162 280 Degree 4: 1 1 1 4 5 6 7 32 45 60 Degree 5: 1 1 1 1 5 6 7 8 9 50
Julia
{{works with|Julia|0.6}}
function multifact(n::Integer, k::Integer) n > 0 && k > 0 || throw(DomainError()) k > 1 || factorial(n) return prod(n:-k:2) end const khi = 5 const nhi = 10 println("Showing multifactorial for n in [1, $nhi] and k in [1, $khi].") for k = 1:khi a = multifact.(1:nhi, k) lab = "n" * "!" ^ k @printf(" %-6s → %s\n", lab, a) end
{{out}}
Showing multifactorial for n in [1, 10] and k in [1, 5].
n! → [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
n!! → [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
n!!! → [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
n!!!! → [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
n!!!!! → [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
Kotlin
fun multifactorial(n: Long, d: Int) : Long { val r = n % d return (1..n).filter { it % d == r } .reduce { i, p -> i * p } } fun main(args: Array<String>) { val m = 5 val r = 1..10L for (d in 1..m) { print("%${m}s:".format( "!".repeat(d))) r.forEach { print(" " + multifactorial(it, d)) } println() } }
{{Out}}
!: 1 2 6 24 120 720 5040 40320 362880 3628800
!!: 1 2 3 8 15 48 105 384 945 3840
!!!: 1 2 3 4 10 18 28 80 162 280
!!!!: 1 2 3 4 5 12 21 32 45 120
!!!!!: 1 2 3 4 5 6 14 24 36 50
Lua
function multiFact (n, degree) local fact = 1 for i = n, 2, -degree do fact = fact * i end return fact end print("Degree\t|\tMultifactorials 1 to 10") print(string.rep("-", 52)) for d = 1, 5 do io.write(" " .. d, "\t| ") for n = 1, 10 do io.write(multiFact(n, d) .. " ") end print() end
{{out}}
Degree | Multifactorials 1 to 10
----------------------------------------------------
1 | 1 2 6 24 120 720 5040 40320 362880 3628800
2 | 1 2 3 8 15 48 105 384 945 3840
3 | 1 2 3 4 10 18 28 80 162 280
4 | 1 2 3 4 5 12 21 32 45 120
5 | 1 2 3 4 5 6 14 24 36 50
Maple
{{output?|Maple}}
f := proc (n, m)
local fac, i;
fac := 1;
for i from n by -m to 1 do
fac := fac*i;
end do;
return fac;
end proc:
a:=Matrix(5,10):
for i from 1 to 5 do
for j from 1 to 10 do
a[i,j]:=f(j,i);
end do;
end do;
a;
Mathematica
Multifactorial[n_, m_] := Abs[ Apply[ Times, Range[-n, -1, m]]]
Table[ Multifactorial[j, i], {i, 5}, {j, 10}] // TableForm
{{out}}
1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50
min
{{works with|min|0.19.3}}
(:d (dup 0 <=) (pop 1) (dup d -) (*) linrec) :multifactorial
(:d 1 (dup d multifactorial print! " " print! succ) 10 times newline pop) :row
1 (dup "Degree " print! print ": " print! row succ) 5 times
{{out}}
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
=={{header|МК-61/52}}==
Instruction: ''number'' ^ ''degree'' В/О С/П
## Nim
```nim
# Recursive
proc multifact(n, deg): int =
result = (if n <= deg: n else: n * multifact(n - deg, deg))
# Iterative
proc multifactI(n, deg): int =
result = n
var n = n
while n >= deg + 1:
result *= n - deg
n -= deg
for i in 1..5:
stdout.write "\nDegree ", i, ": "
for j in 1..10:
stdout.write multifactI(j, i), " "
Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
Objeck
{{trans|C}}
class Multifact {
function : MultiFact(n : Int, deg : Int) ~ Int {
result := n;
while (n >= deg + 1){
result *= (n - deg);
n -= deg;
};
return result;
}
function : Main(args : String[]) ~ Nil {
for (i := 1; i <= 5; i+=1;){
IO.Console->Print("Degree ")->Print(i)->Print(": ");
for (j := 1; j <= 10; j+=1;){
IO.Console->Print(' ')->Print(MultiFact(j, i));
};
IO.Console->PrintLine();
};
}
}
Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
Oforth
: multifact(n, deg) 1 while( n 0 > ) [ n * n deg - ->n ] ;
: printMulti
| i |
5 loop: i [ System.Out i << " : " << 10 seq map(#[ i multifact]) << cr ] ;
{{out}}
1 : [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
2 : [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
3 : [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
4 : [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
5 : [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
PARI/GP
fac(n,d)=prod(k=0,(n-1)\d,n-k*d)
for(k=1,5,for(n=1,10,print1(fac(n,k)" "));print)
1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50
Perl
{ # <-- scoping the cache and bigint clause my @cache; use bigint; sub mfact { my ($s, $n) = @_; return 1 if $n <= 0; $cache[$s][$n] //= $n * mfact($s, $n - $s); } } for my $s (1 .. 10) { print "step=$s: "; print join(" ", map(mfact($s, $_), 1 .. 10)), "\n"; }
{{out}}
step=1: 1 2 6 24 120 720 5040 40320 362880 3628800
step=2: 1 2 3 8 15 48 105 384 945 3840
step=3: 1 2 3 4 10 18 28 80 162 280
step=4: 1 2 3 4 5 12 21 32 45 120
step=5: 1 2 3 4 5 6 14 24 36 50
step=6: 1 2 3 4 5 6 7 16 27 40
step=7: 1 2 3 4 5 6 7 8 18 30
step=8: 1 2 3 4 5 6 7 8 9 20
step=9: 1 2 3 4 5 6 7 8 9 10
step=10: 1 2 3 4 5 6 7 8 9 10
We can also do this iteratively. ntheory's vecprod makes bigint products if needed, so we don't have to worry about it. {{libheader|ntheory}}
use ntheory qw/vecprod/; sub mfac { my($n,$d) = @_; vecprod(map { $n - $_*$d } 0 .. int(($n-1)/$d)); } for my $degree (1..5) { say "$degree: ",join(" ",map{mfac($_,$degree)} 1..10); }
{{out}}
1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50
Perl 6
for 1 .. 5 -> $degree {
sub mfact($n) { [*] $n, *-$degree ...^ * <= 0 };
say "$degree: ", map &mfact, 1..10
}
{{out}}
1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50
Phix
function multifactorial(integer n, integer order)
atom res = 1
if n>0 then
res = n*multifactorial(n-order,order)
end if
return res
end function
sequence s = repeat(0,10)
for i=1 to 5 do
for j=1 to 10 do
s[j] = multifactorial(j,i)
end for
?s
end for
{{out}}
{1,2,6,24,120,720,5040,40320,362880,3628800}
{1,2,3,8,15,48,105,384,945,3840}
{1,2,3,4,10,18,28,80,162,280}
{1,2,3,4,5,12,21,32,45,120}
{1,2,3,4,5,6,14,24,36,50}
PicoLisp
{{trans|C}}
(de multifact (N Deg)
(let Res N
(while (> N Deg)
(setq Res (* Res (dec 'N Deg))) )
Res ) )
(for I 5
(prin "Degree " I ":")
(for J 10
(prin " " (multifact J I)) )
(prinl) )
Output:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
PL/I
do i = 1 to 5; put skip edit (substr(text, 1, i+1), '=' ) (A, COLUMN(8)); do n = 1 to 10; put edit ( trim( multifactorial(n,i) ) ) (X(1), A); end; end;
multifactorial: procedure (n, j) returns (fixed(15)); declare (n, j) fixed binary; declare f fixed (15), m fixed(15);
f, m = n; do while (m > j); f = f * (m-fixed(j)); m = m - j; end; return (f);
end multifactorial;
end multi;
Output:
```txt
n! = 1 2 6 24 120 720 5040 40320 362880 3628800
n!! = 1 2 3 8 15 48 105 384 945 3840
n!!! = 1 2 3 4 10 18 28 80 162 280
n!!!! = 1 2 3 4 5 12 21 32 45 120
n!!!!! = 1 2 3 4 5 6 14 24 36 50
plainTeX
Works with an etex engine.
\long\def\antefi#1#2\fi{#2\fi#1} \def\fornum#1=#2to#3(#4){% \edef#1{\number\numexpr#2}\edef\fornumtemp{\noexpand\fornumi\expandafter\noexpand\csname fornum\string#1\endcsname {\number\numexpr#3}{\ifnum\numexpr#4<0 <\else>\fi}{\number\numexpr#4}\noexpand#1}\fornumtemp } \long\def\fornumi#1#2#3#4#5#6{\def#1{\unless\ifnum#5#3#2\relax\antefi{#6\edef#5{\number\numexpr#5+(#4)\relax}#1}\fi}#1} \newcount\result \def\multifact#1#2{% \result=1 \fornum\multifactiter=#1 to 1(-#2){\multiply\result\multifactiter}% \number\result } \fornum\degree=1 to 5(+1){Degree \degree: \fornum\ii=1 to 10(+1){\multifact\ii\degree\space\space}\par} \bye
Output pdf looks like:
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
Python
Python: Iterative
from functools import reduce
>>> from operator import mul
>>> def mfac(n, m): return reduce(mul, range(n, 0, -m))
>>> for m in range(1, 11): print("%2i: %r" % (m, [mfac(n, m) for n in range(1, 11)]))
1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
6: [1, 2, 3, 4, 5, 6, 7, 16, 27, 40]
7: [1, 2, 3, 4, 5, 6, 7, 8, 18, 30]
8: [1, 2, 3, 4, 5, 6, 7, 8, 9, 20]
9: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
10: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
>>>
Python: Recursive
def mfac2(n, m): return n if n <= (m + 1) else n * mfac2(n - m, m)
>>> for m in range(1, 6): print("%2i: %r" % (m, [mfac2(n, m) for n in range(1, 11)]))
1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
>>>
R
#x is Input #n is Factorial Number multifactorial=function(x,n){ if(x<=n+1){ return(x) }else{ return(x*multifactorial(x-n,n)) } }
Racket
#lang racket
(define (multi-factorial-fn m)
(lambda (n)
(let inner ((acc 1) (n n))
(if (<= n m) (* acc n)
(inner (* acc n) (- n m))))))
;; using (multi-factorial-fn m) as a first-class function
(for*/list ([m (in-range 1 (add1 5))] [mf-m (in-value (multi-factorial-fn m))])
(for/list ([n (in-range 1 (add1 10))])
(mf-m n)))
(define (multi-factorial m n) ((multi-factorial-fn m) n))
(for/list ([m (in-range 1 (add1 5))])
(for/list ([n (in-range 1 (add1 10))])
(multi-factorial m n)))
Output:
'((1 2 6 24 120 720 5040 40320 362880 3628800)
(1 2 3 8 15 48 105 384 945 3840)
(1 2 3 4 10 18 28 80 162 280)
(1 2 3 4 5 12 21 32 45 120)
(1 2 3 4 5 6 14 24 36 50))
'((1 2 6 24 120 720 5040 40320 362880 3628800)
(1 2 3 8 15 48 105 384 945 3840)
(1 2 3 4 10 18 28 80 162 280)
(1 2 3 4 5 12 21 32 45 120)
(1 2 3 4 5 6 14 24 36 50))
REXX
This version also handles zero as well as positive integers.
/*REXX program calculates and displays K-fact (multifactorial) of non-negative integers.*/
numeric digits 1000 /*get ka-razy with the decimal digits. */
parse arg num deg . /*get optional arguments from the C.L. */
if num=='' | num=="," then num=15 /*Not specified? Then use the default.*/
if deg=='' | deg=="," then deg=10 /* " " " " " " */
say '═══showing multiple factorials (1 ──►' deg") for numbers 1 ──►" num
say
do d=1 for deg /*the factorializing (degree) of !'s.*/
_= /*the list of factorials (so far). */
do f=1 for num /* ◄── perform a ! from 1 ───► number.*/
_=_ Kfact(f, d) /*build a list of factorial products.*/
end /*f*/ /* [↑] D can default to unity. */
say right('n'copies("!", d), 1+deg) right('['d"]", 2+length(num) )':' _
end /*d*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Kfact: procedure; !=1; do j=arg(1) to 2 by -word(arg(2) 1,1); !=!*j; end; return !
'''output''' when using the default input:
═══showing multiple factorials (1 ──► 10) for numbers 1 ──► 15
n! [1]: 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
n!! [2]: 1 2 3 8 15 48 105 384 945 3840 10395 46080 135135 645120 2027025
n!!! [3]: 1 2 3 4 10 18 28 80 162 280 880 1944 3640 12320 29160
n!!!! [4]: 1 2 3 4 5 12 21 32 45 120 231 384 585 1680 3465
n!!!!! [5]: 1 2 3 4 5 6 14 24 36 50 66 168 312 504 750
n!!!!!! [6]: 1 2 3 4 5 6 7 16 27 40 55 72 91 224 405
n!!!!!!! [7]: 1 2 3 4 5 6 7 8 18 30 44 60 78 98 120
n!!!!!!!! [8]: 1 2 3 4 5 6 7 8 9 20 33 48 65 84 105
n!!!!!!!!! [9]: 1 2 3 4 5 6 7 8 9 10 22 36 52 70 90
n!!!!!!!!!! [10]: 1 2 3 4 5 6 7 8 9 10 11 24 39 56 75
Ring
see "Degree " + "|" + " Multifactorials 1 to 10" + nl
see copy("-", 52) + nl
for d = 1 to 5
see "" + d + " " + "| "
for n = 1 to 10
see "" + multiFact(n, d) + " "
next
see nl
next
func multiFact n, degree
fact = 1
for i = n to 2 step -degree
fact = fact * i
next
return fact
Output:
Degree | Multifactorials 1 to 10
----------------------------------------------------
1 | 1 2 6 24 120 720 5040 40320 362880 3628800
2 | 1 2 3 8 15 48 105 384 945 3840
3 | 1 2 3 4 10 18 28 80 162 280
4 | 1 2 3 4 5 12 21 32 45 120
5 | 1 2 3 4 5 6 14 24 36 50
Ruby
def multifact(n, d) n.step(1, -d).inject( :* ) end (1..5).each {|d| puts "Degree #{d}: #{(1..10).map{|n| multifact(n, d)}.join "\t"}"}
'''output'''
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
```
=
## Run BASIC
=
```runbasic
print "Degree " + "|" + " Multifactorials 1 to 10" + nl
print copy("-", 52) + nl
for d = 1 to 5
print "" + d + " " + "| "
for n = 1 to 10
print "" + multiFact(n, d) + " ";
next
print
next
function multiFact(n,degree)
fact = 1
for i = n to 2 step -degree
fact = fact * i
next
multiFact = fact
end function
```
```txt
Degree | Multifactorials 1 to 10
--------|---------------------------------------------
1 | 1 2 6 24 120 720 5040 40320 362880 3628800
2 | 1 2 3 8 15 48 105 384 945 3840
3 | 1 2 3 4 10 18 28 80 162 280
4 | 1 2 3 4 5 12 21 32 45 120
5 | 1 2 3 4 5 6 14 24 36 50
```
## Scala
```scala
def multiFact(n : BigInt, degree : BigInt) = (n to 1 by -degree).product
for{
degree <- 1 to 5
str = (1 to 10).map(n => multiFact(n, degree)).mkString(" ")
} println(s"Degree $degree: $str")
```
{{out}}
```txt
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
```
## Scheme
```scheme
(import (scheme base)
(scheme write)
(srfi 1))
(define (multi-factorial n m)
(fold * 1 (iota (ceiling (/ n m)) n (- m))))
(for-each
(lambda (degree)
(display (string-append "degree "
(number->string degree)
": "))
(for-each
(lambda (num)
(display (string-append (number->string (multi-factorial num degree))
" ")))
(iota 10 1))
(newline))
(iota 5 1))
```
{{out}}
```txt
degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
degree 2: 1 2 3 8 15 48 105 384 945 3840
degree 3: 1 2 3 4 10 18 28 80 162 280
degree 4: 1 2 3 4 5 12 21 32 45 120
degree 5: 1 2 3 4 5 6 14 24 36 50
```
## Seed7
```seed7
$ include "seed7_05.s7i";
const func integer: multiFact (in var integer: num, in integer: degree) is func
result
var integer: multiFact is 1;
begin
while num > 1 do
multiFact *:= num;
num -:= degree;
end while;
end func;
const proc: main is func
local
var integer: degree is 0;
var integer: num is 0;
begin
for degree range 1 to 5 do
write("Degree " <& degree <& ": ");
for num range 1 to 10 do
write(multiFact(num, degree) <& " ");
end for;
writeln;
end for;
end func;
```
{{out}}
```txt
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
```
## Sidef
```ruby
func mfact(s, n) {
n > 0 ? (n * mfact(s, n-s)) : 1
}
{ |s|
say "step=#{s}: #{{|n| mfact(s, n)}.map(1..10).join(' ')}"
} << 1..10
```
{{out}}
```txt
step=1: 1 2 6 24 120 720 5040 40320 362880 3628800
step=2: 1 2 3 8 15 48 105 384 945 3840
step=3: 1 2 3 4 10 18 28 80 162 280
step=4: 1 2 3 4 5 12 21 32 45 120
step=5: 1 2 3 4 5 6 14 24 36 50
step=6: 1 2 3 4 5 6 7 16 27 40
step=7: 1 2 3 4 5 6 7 8 18 30
step=8: 1 2 3 4 5 6 7 8 9 20
step=9: 1 2 3 4 5 6 7 8 9 10
step=10: 1 2 3 4 5 6 7 8 9 10
```
## Swift
```swift
func multiFactorial(_ n: Int, k: Int) -> Int {
return stride(from: n, to: 0, by: -k).reduce(1, *)
}
let multis = (1...5).map({degree in
(1...10).map({member in
multiFactorial(member, k: degree)
})
})
for (i, degree) in multis.enumerated() {
print("Degree \(i + 1): \(degree)")
}
```
{{out}}
```txt
Degree 1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
Degree 2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
Degree 3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
Degree 4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
Degree 5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
```
## Tcl
{{works with|Tcl|8.6}}
```tcl
package require Tcl 8.6
proc mfact {n m} {
set mm [expr {-$m}]
for {set r $n} {[incr n $mm] > 1} {set r [expr {$r * $n}]} {}
return $r
}
foreach n {1 2 3 4 5 6 7 8 9 10} {
puts $n:[join [lmap m {1 2 3 4 5 6 7 8 9 10} {mfact $m $n}] ,]
}
```
{{out}}
```txt
1:1,2,6,24,120,720,5040,40320,362880,3628800
2:1,2,3,8,15,48,105,384,945,3840
3:1,2,3,4,10,18,28,80,162,280
4:1,2,3,4,5,12,21,32,45,120
5:1,2,3,4,5,6,14,24,36,50
6:1,2,3,4,5,6,7,16,27,40
7:1,2,3,4,5,6,7,8,18,30
8:1,2,3,4,5,6,7,8,9,20
9:1,2,3,4,5,6,7,8,9,10
10:1,2,3,4,5,6,7,8,9,10
```
## uBasic/4tH
{{Trans|Run BASIC}}
print "Degree | Multifactorials 1 to 10"
for x = 1 to 53 : print "-"; : next : print
for d = 1 to 5
print d;" ";"| ";
for n = 1 to 10
print FUNC(_multiFact(n, d));" ";
next
print
next
end
_multiFact param (2)
local (2)
c@ = 1
for d@ = a@ to 2 step -b@
c@ = c@ * d@
next
return (c@)
```
{{Out}}
```txt
Degree | Multifactorials 1 to 10
-----------------------------------------------------
1 | 1 2 6 24 120 720 5040 40320 362880 3628800
2 | 1 2 3 8 15 48 105 384 945 3840
3 | 1 2 3 4 10 18 28 80 162 280
4 | 1 2 3 4 5 12 21 32 45 120
5 | 1 2 3 4 5 6 14 24 36 50
0 OK, 0:1063
```
## VBScript
```vb
Function multifactorial(n,d)
If n = 0 Then
multifactorial = 1
Else
For i = n To 1 Step -d
If i = n Then
multifactorial = n
Else
multifactorial = multifactorial * i
End If
Next
End If
End Function
For j = 1 To 5
WScript.StdOut.Write "Degree " & j & ": "
For k = 1 To 10
If k = 10 Then
WScript.StdOut.Write multifactorial(k,j)
Else
WScript.StdOut.Write multifactorial(k,j) & " "
End If
Next
WScript.StdOut.WriteLine
Next
```
{{Out}}
```txt
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
```
## Wortel
```wortel
@let {
facd &[d n]?{<= n d n @prod@range[n 1 @-d]}
; tacit implementation
facdt ^(!?(/^> .1 ^(@prod @range ~1jdtShj &^!(@- @id))) @,)
; recursive
facdrec &[n d] ?{<= n d n *n !!facdrec -n d d}
; output
l @to 10
~@each @to 5 &n !console.log "Degree {n}: {@join @s !*\facd n l}"
}
```
Output
```txt
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50
```
## XPL0
```XPL0
code ChOut=8, CrLf=9, IntOut=11;
func MultiFac(N, D); \Return multifactorial of N in degree D
int N, D;
int F;
[F:= 1;
repeat F:= F*N;
N:= N-D;
until N <= 1;
return F;
];
int I, J; \generate table of multifactorials
for J:= 1 to 5 do
[for I:= 1 to 10 do
[IntOut(0, MultiFac(I, J)); ChOut(0, 9\tab\)];
CrLf(0);
]
```
{{out}}
```txt
1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50
```
## zkl
```zkl
fcn mfact(n,m){ [n..1,-m].reduce('*,1) }
foreach m in ([1..5]){ println("%d: %s".fmt(m,[1..10].apply(mfact.fp1(m)))) }
```
{{out}}
```txt
1: L(1,2,6,24,120,720,5040,40320,362880,3628800)
2: L(1,2,3,8,15,48,105,384,945,3840)
3: L(1,2,3,4,10,18,28,80,162,280)
4: L(1,2,3,4,5,12,21,32,45,120)
5: L(1,2,3,4,5,6,14,24,36,50)
```