Journal of Integer Sequences, Vol. 16 (2013), Article 13.5.1

On the Central Coefficients of Riordan Matrices

Paul Barry
School of Science
Waterford Institute of Technology


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 $\binom{3n}{n}$.

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(Concerned with sequences A000045 A000108 A000984 A001850 A005809 A007318 A084774 A092392 A174687.)

Received January 2 2013; revised version received May 2 2013. Published in Journal of Integer Sequences, May 8 2013.

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