The central factorials x^[k] form an associated Sheffer sequence with f(t) | = | e^(t/2) - e^(-t/2) | = | 2sinh(1/2 t), giving the generating function sum_(k = 0)^∞ x^[k]/(k!) t^k = e^(2x sinh^(-1)(t/2)).

factorial | falling factorial | Gould polynomial | rising factorial