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
Portugal
Pasquale Petrullo
Dipartimento di Matematica e Informatica
Università degli Studi della Basilicata
Potenza
Italy
Abstract:
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.
Full version: pdf,
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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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