Mark Shattuck

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 4, Pages 74—80

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## Details

### 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

### References

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*r*-Lah numbers, Discrete Math., http://dx.doi.org/10.1016/j.disc.2014.03.029 (in press). - Stanley, R. P. (1997) Enumerative Combinatorics, Vol. I, Cambridge University Press.
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## Cite this paper

APAShattuck, M. (2015). A generalized recurrence formula for Stirling numbers and related sequences. Notes on Number Theory and Discrete Mathematics, 21(4), 74-80.

ChicagoShattuck, Mark. “A Generalized Recurrence Formula for Stirling Numbers and Related Sequences.” Notes on Number Theory and Discrete Mathematics 21, no. 4 (2015): 74-80.

MLAShattuck, Mark. “A Generalized Recurrence Formula for Stirling Numbers and Related Sequences.” Notes on Number Theory and Discrete Mathematics 21.4 (2015): 74-80. Print.