number of permutations with a given cycle structure

[Max Alekseyev <maxale@gmail.com>]

Hello,

Any integer partition p of n can be treated as a cycle type of the permutations of n, and the number of those permutations is a fundamental function of p that would be nice to have handy in PARI.

Just in case, an explicit formula for this function can be seen in https://en.wikipedia.org/wiki/Permutation#Cycle_type

I was not able to find it in PARI, and if it's indeed missing, could you please add it?

On a related note, I'd appreciate it if this function is not restricted to t_VECSMALL type, but can also accept t_VEC.

I already see trouble with that in permcycles() when a permutation is manually constructed as t_VEC. Btw, can permcycles() be made to accept t_VEC as well?

Thanks,

Max