Function generating_tuple_count 

pub fn generating_tuple_count(
    degree: usize,
    gens: &[Perm],
    cap: usize,
    k: u32,
) -> Option<i128>

The number of ordered k-tuples of group elements that generate G — the Eulerian function e_k(G) = Σ_{H ≤ G} μ(H, G)·|H|ᵏ (Hall’s formula by Möbius inversion over the subgroup lattice, since |H|ᵏ counts the k-tuples landing in H). Dividing by |G|ᵏ gives the probability that k random elements generate G. None when |G| > cap.