On the Inverses of a Family of Pascal-Like Matrices Defined by Riordan Arrays
School of Science
Waterford Institute of Technology
We study a number of characteristics of the inverses of the elements of
a family of Pascal-like matrices that are defined by Riordan arrays. We
give several forms of the bivariate generating function of these
inverses, along with four different closed-form expressions for the
general element of the inverse. We study the row sums and the diagonal
sums of the inverses, and the first column sequence. We exhibit the
elements of the first column sequence of the inverse matrix as the
moments of a family of orthogonal polynomials, whose coefficient array
is again a Riordan array. We also give the Hankel transform of these
latter sequences. Other related sequences are also studied.
Full version: pdf,
(Concerned with sequences
Received January 15 2013;
revised versions received April 15 2013; May 6 2013.
Published in Journal of Integer Sequences, May 25 2013.
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