Barry, Paul

On a family of generalized Pascal triangles defined by exponential Riordan arrays

J. Integer Seq. 10(3), Article 07.3.5, 21 p., electronic only (2007)


Summary: We introduce a family of number triangles defined by exponential Riordan arrays, which generalize Pascal's triangle. We characterize the row sums and central coefficients 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.

Mathematics Subject Classification

11B83, 05A19, 33C45, 11B37, 11B65


Pascal's triangle, narayana numbers, Catalan numbers, lah numbers, Hermite polynomials, Laguerre polynomials, Bessel polynomials