Factorizations of large cycles in the symmetric group (Q1613557)

Let \(C^{(n)}_{\alpha_1,\dots,\alpha_m}\) denote the number of factorizations of an \(n\)-cycle into \(m\) permutations of \(S_n\) of types \(\alpha_1,\dots,\alpha_m\). Although this number can be computed using the character table of \(S_n\), but the authors find a new formula to calculate this number.