Resumen de Racional identities in the Catalan triangle

Pedro José Miana Sanz , Natalia Romero

• In this paper we consider different racional identities in which appear the numbers (Bn,p)n,1≤p≤n given by Bn,p := pn 2n n − p, n, p 2 N, p  n.

  The set of numbers (Bn,p)n,1≤p≤n is known as the Catalan triangle due to the Catalan numbers (Cn)n∈N,Cn = 1 n + 12n n , n 2 N, appear in the first column. These identities have been recently proved and some of them are connected with the dynamic behavior of certain iterative methods applied to quadratic polynomials. In the last section we conjeture some new identities which involve this family of numbers (Bn,p)n,1≤p≤n.