Journal of Integer Sequences, Vol. 14 (2011), Article 11.8.2

Generalized Stirling Numbers, Exponential Riordan Arrays, and Orthogonal Polynomials

Aoife Hennessy
Department of Computing, Mathematics and Physics
Waterford Institute of Technology

Paul Barry
School of Science
Waterford Institute of Technology


We define a generalization of the Stirling numbers of the second kind, which depends on two parameters. The matrices of integers that result are exponential Riordan arrays. We explore links to orthogonal polynomials by studying the production matrices of these Riordan arrays. Generalized Bell numbers are also defined, again depending on two parameters, and we determine the Hankel transform of these numbers.

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(Concerned with sequences A000007 A000045 A000108 A000262 A007318 A048894 A048993 A048994 A049020 A056857 A094587 A094816 A111596 A111884.)

Received April 15 2011; revised version received August 10 2011. Published in Journal of Integer Sequences, September 25 2011.

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