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.
On One-Parameter Catalan Arrays
Petrullo, P
2015-01-01
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.File in questo prodotto:
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