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Extended Bell and Stirling numbers from hypergeometric exponentiation

By J. -M. Sixdeniers, K. A. Penson and A. I. Solomon

Abstract

Exponentiating the hypergeometric series \ud <sub>0</sub>F<sub>L</sub>(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences \ud b<sub>L</sub>(n), n = 0,1,2,.... For L >= 0, the b<sub>L</sub>(n)'s are generalizations of the conventional Bell numbers, b<sub>0</sub>(n). The corresponding associated Stirling numbers of the second kind are also investigated. For L = 1 one can give a combinatorial interpretation of the numbers b<sub>1</sub>(n) and of some Stirling numbers associated with them. We also consider the L>1 analogues of Bell numbers for restricted partitions

Year: 2001
OAI identifier: oai:oro.open.ac.uk:8160
Provided by: Open Research Online

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