The Open UniversitySkip to content

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)

Full text available as:
PDF (Not Set) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (178kB)
Google Scholar: Look up in Google Scholar


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 Item
Copyright Holders: 2001 The Authors
ISSN: 1530-7638
Extra Information: 11 pp.
Keywords: integer sequences; Bell numbers; Stirling numbers; hypergeometric series
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 8160
Depositing User: Allan Solomon
Date Deposited: 21 Jun 2007
Last Modified: 02 May 2018 12:45
Share this page:

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU