No abstract

We study three sequences of polynomials defined as successive derivatives with respect to a differential operator associated with a grammar (one of these sequences was originally introduced by Ramanujan). Combinatorial interpretations for these polynomials are found in terms of rooted trees and graphs of mappings from $[n]$ to $[n]$.

No abstract

Summary. We characterize the ordinary generating functions of the Genocchi and median Genoochi numbers as unique solutions of some functional equations and give a direct algebraic proof of several continued fraction expansions for these functions. New relations between these numbers are also obtained.

No abstract