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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
0_F_L(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences
b_L(n), n = 0,1,2,.... For L >= 0, the b_L(n)'s are generalizations of the conventional Bell numbers, b_0(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_1(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
ISSN: 1530-7638
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: 09 Dec 2010 06:25
URI: http://oro.open.ac.uk/id/eprint/8160
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