New identities in the Catalan triangle

In this paper we prove new identities in the Catalan triangle whose (n,p)(n,p) entry is defined byBn,p:=pn(2nn−p),n,p∈N,p⩽n. In fact, we show some new identities involving the well-known Catalan numbers, and specially the identity∑p=1iBn,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.