On the Central Coefficients of Riordan Matrices

Barry, Paul (2013) On the Central Coefficients of Riordan Matrices. Journal of Integer Sequences, 16. ISSN 1530-7638

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Abstract

We use the Lagrange-Bürmann inversion theorem to characterize the generating function of the central coefficients of the elements of the Riordan group of matrices. We apply this result to calculate the generating function of the central elements of a number of explicit Riordan arrays, defined by rational expressions, and in two cases we use the generating functions thus found to calculate the Hankel transforms of the central elements, which are themselves expressible as combinatorial polynomials. We finally look at two cases of Riordan arrays defined by non-rational expressions. The last example uses our methods to calculate the generating function of $\binom{3n}{n}$.

Item Type: Article
Departments or Groups: *NONE OF THESE*
Depositing User: Paul Barry
Date Deposited: 16 May 2013 18:39
Last Modified: 22 Aug 2016 10:26
URI: http://repository.wit.ie/id/eprint/2647

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