New identities in the Catalan triangle.

  1. Gutiérrez, J.M. 1
  2. Hernández, M.A. 1
  3. Miana, P.J. 2
  4. Romero, N. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

Revista:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Any de publicació: 2008

Volum: 341

Número: 1

Pàgines: 52-61

Tipus: Article

beta Ver similares en nube de resultados
DOI: 10.1016/J.JMAA.2007.09.073 SCOPUS: 2-s2.0-38749113742 WoS: WOS:000253868000004 GOOGLE SCHOLAR

Altres publicacions en: Journal of Mathematical Analysis and Applications

Repositori institucional: lock_openAccés obert Editor

Objectius de Desenvolupament Sostenible

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Resum

In this paper we prove new identities in the Catalan triangle whose (n, p) entry is defined byB n, p : = frac(p, n) ((2 n; n - p)), n, p ∈ N, p ≤ n . In fact, we show some new identities involving the well-known Catalan numbers, and specially the identityunderover(∑, p = 1, i) B n, p B n, n + p - i (n + 2 p - i) = (n + 1) C n ((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.