On the Central Coefficients of Riordan Matrices

Paul Barry

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

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 $\binom{3n}{n}$.
Original languageEnglish
JournalJournal of Integer Sequences
Volume16
Issue number5
DOIs
Publication statusPublished - 08 May 2013

Keywords

  • Central coefficients
  • Hankel transform
  • Integer sequence
  • Lagrange inversion
  • Riordan group

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