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New identities in the Catalan triangle

New identities in the Catalan triangle,10.1016/j.jmaa.2007.09.073,Journal of Mathematical Analysis and Applications,J. M. Gutiérrez,M. A. Hernández,P.

New identities in the Catalan triangle   (Citations: 8)
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In this paper we prove new identities in the Catalan triangle whose (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.
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    • ...In [5], Gutierrez, Hernandez, Miana and Romero gave an alternative proof of identities (2) and (3) and established the following identities:...

    Zhizheng Zhanget al. Several identities in the Catalan triangle

    • ...These identities follow easily (see e.g. [3]) from the standard formula...
    • ...(this agrees with the formula given in [3]),...
    • ...The numbers Bn,l appear in several combinatorial problems and identities (see e.g. [6], [3], [2])...
    • ...The authors of the paper [3] have pointed out a relation of these numbers to a problem of the dynamical behavior of a family of iterative methods applied to quadratic polynomials...

    Anton ´ inet al. Identities with squares of binomial coecients

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