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)

URL: http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDE...

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.

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About

• Item ORO ID
• 8160
• Item Type
• Journal Item
• ISSN
• 1530-7638
• Extra Information
• 11 pp.
• Keywords
• integer sequences; Bell numbers; Stirling numbers; hypergeometric series
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2001 The Authors
• Depositing User
• Allan Solomon