New identities in the Catalan triangle

In this paper we prove new identities in the Catalan triangle whose (n,p) entry is defined by Bn,p := p n 2n n− p , n,p ∈ N, p n. In fact, we show some new identities involving the well-known Catalan numbers, and specially the identity i p=1 Bn,pBn,n+p−i(n+ 2p −i) = (n+ 1)Cn 2(n −1) i −1 , i n, that appears in a problem related with the dynamical behavior of a family of iterative methods applied to quadratic polynomials. © 2007 Elsevier Inc. All rights reserved.