 # C++: Multifactorial The factorial of a number, written as n! is defined as n! = n(n − 1)(n − 2)…(2)(1)

A generalization of this is the multifactorials where:

n! = n(n − 1)(n − 2)…(2)(1)
n!! = n(n − 2)(n − 4)…
n!!! = n(n − 3)(n − 6)…
n!!!! = n(n − 4)(n − 8)…
n!!!!! = n(n − 5)(n − 10)…
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

1. Write a function that given n and the degree, calculates the multifactorial.
2. 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, 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.