A generalized recurrence formula for Stirling numbers and related sequences

Mark Shattuck
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 4, Pages 74–80
Full paper (PDF, 157 Kb)

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Authors and affiliations

Mark Shattuck
Department of Mathematics, University of Tennessee
37996 Knoxville, TN, USA

Abstract

In this note, we provide a combinatorial proof of a generalized recurrence formula satisfied by the Stirling numbers of the second kind. We obtain two extensions of this formula, one in terms of r-Whitney numbers and another in terms of q-Stirling numbers of Carlitz. Modifying our proof yields analogous formulas satisfied by the r-Stirling numbers of the first kind and by the r-Lah numbers.

Keywords

• Stirling numbers
• r-Whitney numbers
• q-Stirling numbers

AMS Classification

• 05A19
• 05A18

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