Some combinatorial identities via Stirling transform

Fouad Bounebirat, Diffalah Laissaoui and Mourad Rahmani
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 4, Pages 92—98
DOI: 10.7546/nntdm.2018.24.4.92-98
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Authors and affiliations

Fouad Bounebirat
USTHB, Faculty of Mathematics
P. O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria

Diffalah Laissaoui
Dr Yahia Fares University of Medea
M´ed´ea 26000, Algeria

Mourad Rahmani
USTHB, Faculty of Mathematics
P. O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria

Abstract

The aim of this paper is to present some results on the use of the generalized Stirling transform. First, we establish a generalization of a recent Guo–Qi’s identity for Bell numbers. Finally, a new explicit formula for Euler numbers are given.

Keywords

  • Bell numbers
  • Lah numbers
  • Stirling transform

2010 Mathematics Subject Classification

  • 11B73
  • 33C05

References

  1. Broder, A. Z. (1984). The r-Stirling numbers, Discrete Math., 49, 241–259.
  2. Comtet, L. (1974). Advanced Combinatorics. Reidel Publishing Co., Dordrecht.
  3. Graham, R. L., Knuth, D. E., & Patashnik, O. (1994) Concrete Mathematics. Addison-Wesley Publishing Company, Reading, MA.
  4. Guo, B., & Qi, F. (2014). An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions, Glob. J. Math. Anal., 2, 243–248.
  5. Qi, F. (2016). An explicit formula for the Bell numbers in terms of the Lah and Stirling numbers, Mediterr. J. Math. 13, 2795–2800.
  6. Rahmani, M. (2014). Generalized Stirling transform, Miskolc Math. Notes, 15, 677–690.
  7. Wei, C.-F. & Qi, F. (2015). Several closed expressions for the Euler numbers. J. Inequal. Appl., 219, 8 pp.

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Cite this paper

APA

Bounebirat, F., Laissaoui, D., & Rahmani, M. (2018). Some combinatorial identities via Stirling transform. Notes on Number Theory and Discrete Mathematics, 24(4), 92-98, doi: 10.7546/nntdm.2018.24.4.92-98.

Chicago

Bounebirat, Fouad, Diffalah Laissaoui and Mourad Rahmani. “Some Combinatorial Identities via Stirling Transform.” Notes on Number Theory and Discrete Mathematics 24, no. 4 (2018): 92-98, doi: 10.7546/nntdm.2018.24.4.92-98.

MLA

Bounebirat, Fouad, Diffalah Laissaoui and Mourad Rahmani. “Some Combinatorial Identities via Stirling Transform.” Notes on Number Theory and Discrete Mathematics 24.4 (2018): 92-98. Print, doi: 10.7546/nntdm.2018.24.4.92-98.

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