Riordan arrays, generalized Narayana triangles, and series reversion

摘要

Using elements of the group of Riordan arrays we define a family of generalized Narayana triangles and their associated generalized Catalan numbers, and study their links to series reversion. In particular we use Lagrange inversion techniques to determine the generating functions for these generalized Catalan numbers. (C) 2015 Elsevier Inc. All rights reserved.