On a Family of Generalized Pascal Triangles defined by Exponential Riordan Arrays

Paul Barry

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

We introduce a family of number triangles defined by exponential Riordan arrays, which generalize Pascal’s triangle. We characterize the row sums and central coeffi- cients of these triangles, and define and study a set of generalized Catalan numbers. We establish links to the Hermite, Laguerre and Bessel polynomials, as well as links to the Narayana and Lah numbers.
Original languageEnglish
Article number07.3.5
JournalJournal of Integer Sequences
Volume10
Issue number3
Publication statusPublished - 2007

Keywords

  • Bessel polynomials
  • Catalan numbers
  • Hermite polynomials
  • Laguerre polynomials
  • Lah numbers
  • Narayana numbers
  • Pascal's triangle

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