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 ₀F_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, 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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