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Extended Bell and Stirling numbers from hypergeometric exponentiation

Sixdeniers, J. -M.; Penson, K. A. and Solomon, A. I. (2001). Extended Bell and Stirling numbers from hypergeometric exponentiation. Journal of Integer Sequences, 4(1)

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Abstract

Exponentiating the hypergeometric series 0FL(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences bL(n), n = 0,1,2,.... For L >= 0, the bL(n)'s are generalizations of the conventional Bell numbers, b0(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 b1(n) and of some Stirling numbers associated with them. We also consider the L>1 analogues of Bell numbers for restricted partitions.

Item Type: Journal Article
Copyright Holders: 2001 The Authors
ISSN: 1530-7638
Extra Information: 11 pp.
Keywords: integer sequences; Bell numbers; Stirling numbers; hypergeometric series
Academic Unit/Department: Science > Physical Sciences
Item ID: 8160
Depositing User: Allan Solomon
Date Deposited: 21 Jun 2007
Last Modified: 16 Jun 2014 00:51
URI: http://oro.open.ac.uk/id/eprint/8160
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