The polynomials G_n(x;a, b) given by the associated Sheffer sequence with f(t) = e^(a t)(e^(b t) - 1), where b!=0. The inverse function (and therefore generating function) cannot be computed algebraically, but the generating function sum_(k = 0)^∞ (G_k(x;a, b))/(k!) t^k = e^(x f^(-1)(t)) can be given in terms of the sum f^(-1)(t) = sum_(k = 1)^∞ 1/b(-(b + a k)/b k - 1)t^k/k.

central factorial | falling factorial | Sheffer sequence