Geodesic
Generalized Stirling numbers, exponential Riordan arrays, and orthogonal polynomials
Journal of integer sequences, Tome 14 (2011) no. 8
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.
Classification : 11B73, 33C45, 42C05, 15B36, 15B05, 11C20, 11B83
Keywords: integer sequence, Stirling number, Bell number, Riordan array, Hankel transform, orthogonal polynomial 
@article{JIS_2011__14_8_a6,
     author = {Hennessy,  Aoife and Barry,  Paul},
     title = {Generalized {Stirling} numbers, exponential {Riordan} arrays, and orthogonal polynomials},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {8},
     zbl = {1246.11059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_8_a6/}
}
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%A Barry,  Paul
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%J Journal of integer sequences
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Hennessy,  Aoife; Barry,  Paul. Generalized Stirling numbers, exponential Riordan arrays, and orthogonal polynomials. Journal of integer sequences, Tome 14 (2011) no. 8. http://geodesic.mathdoc.fr/item/JIS_2011__14_8_a6/