The central coefficients of a family of pascal-like triangles and colored lattice paths

Paul Barry

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study the central coefficients of a family of Pascal-like triangles defined by Riordan arrays. These central coefficients count left-factors of colored Schröder paths. We give various forms of the generating function, including continued fraction forms, and we calculate their Hankel transform. By using the A and Z sequences of the defining Riordan arrays, we obtain a matrix whose row sums are equal to the central coefficients under study. We explore the row polynomials of this matrix. We give alternative formulas for the coefficient array of the sequence of central coefficients.

Original languageEnglish
Article number19.1.3
JournalJournal of Integer Sequences
Volume22
Issue number1
Publication statusPublished - 2019

Keywords

  • Central binomial coefficient
  • Lattice path
  • Motzkin path
  • Pascal-like triangle
  • Riordan array
  • Schröder path

Fingerprint

Dive into the research topics of 'The central coefficients of a family of pascal-like triangles and colored lattice paths'. Together they form a unique fingerprint.

Cite this