C++: Multifactorial

The factorial of a number, written as $n!$ is defined as $n! = n (n - 1)(n - 2)\dots(2)(1)$

A generalization of this is the multifactorials where:

n! = n (n - 1)(n - 2)\dots(2)(1)

n!! = n (n - 2)(n - 4)\dots

n!!! = n (n - 3)(n - 6)\dots

n!!!! = n (n - 4)(n - 8)\dots

n!!!!! = n (n - 5)(n - 10)\dots

Where the products are for 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 to

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 1..10 members of the first five degrees of multifactorial.

#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;
}

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 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

SOURCE

Content is available under GNU Free Documentation License 1.2.