Journal of Integer Sequences, Vol. 10 (2007), Article 07.3.5

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

Paul Barry
School of Science
Waterford Institute of Technology


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.

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(Concerned with sequences A000085 A000108 A000262 A000898 A001147 A001263 A001498 A001813 A002720 A005425 A007318 A008297 A025167 A025168 A047974 A052852 A0100862 and A0102757 .)

Received January 16 2006; revised version received March 27 2007. Published in Journal of Integer Sequences March 28 2007.

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