Generalized Stirling Numbers, Exponential Riordan Arrays, and Orthogonal Polynomials
Aoife Hennessy
Department of Computing, Mathematics and Physics
Waterford Institute of Technology
Ireland
Paul Barry
School of Science
Waterford Institute of Technology
Ireland
Abstract:
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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