Extended Bell and Stirling numbers from hypergeometric exponentiation

2001/06/14 by J. -M. Sixdeniers, Sixdeniers, J. -M., K. A. Penson +3
Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.math/0106123

12 pages, Latex. Journal of Integer Sequences (in press)

arxiv created 2001/06/14 · arxiv updated 2009/11/30

Abstract

Exponentiating the hypergeometric series gives a recursion relation for integer sequences which are generalizations of conventional Bell numbers. The corresponding associated Stirling numbers of the second kind are also generated and investigated. For the lowest order generalisation, one can give a combinatorial interpretation of these 'Bell' numbers, and of some Stirling numbers associated with them. We also consider these analogues of Bell numbers in the case of restricted partitions.

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• Heterogeneous Stirling numbers and heterogeneous Bell polynomials
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• On Relations Between the Stirling Numbers of First and Second Kind