Problem Statement

The factorial of a number, written as

n !

{\displaystyle n!}

, is defined as

n !

n ( n − 1 ) ( n − 2 ) . . . ( 2 ) ( 1 )

{\displaystyle n!=n(n-1)(n-2)...(2)(1)}

. 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:

Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.

Let's start with the solution:

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;