Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.1

On One-Parameter Catalan Arrays

José Agapito, Ângela Mestre, and Maria M. Torres
Centro de Análise Funcional, Estruturas Lineares e Aplicações
Grupo de Estruturas Algébricas, Lineares e Combinatórias
Departamento de Matemática
Faculdade de Ciências, Universidade de Lisboa
1749-016 Lisboa

Pasquale Petrullo
Dipartimento di Matematica e Informatica
Università degli Studi della Basilicata


We present a parametric family of Riordan arrays, which are obtained by multiplying any Riordan array with a generalized Pascal array. In particular, we focus on some interesting properties of one-parameter Catalan triangles. We obtain several combinatorial identities that involve two special Catalan matrices, the Chebyshev polynomials of the second kind, some periodic sequences, and the Fibonacci numbers.

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(Concerned with sequences A001700 A008549 A033184 A035330 A039598 A045720 A045894 A049027 A076025.)

Received January 27 2015; revised versions received February 17 2015; March 3 2015. Published in Journal of Integer Sequences, May 17 2015.

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