The 2-successive partial Bell polynomials

Meriem Tiachachat and Miloud Mihoubi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 538–544
DOI: 10.7546/nntdm.2023.29.3.538-544
Full paper (PDF, 203 Kb)


Authors and affiliations

Meriem Tiachachat
Department of Operational Research, USTHB
P. O. 32 El Alia 16111 Algiers, Algeria

Miloud Mihoubi
Department of Operational Research, USTHB
P. O. 32 El Alia 16111 Algiers, Algeria


In this paper, we discuss a new class of partial Bell polynomials. The first section gives an overview of partial Bell polynomials and their related 2-successive Stirling numbers. In the second section, we introduce the concept of 2-successive partial Bell polynomials. We give an explicit formula for computing these polynomials and establish their generating function. In addition, we derive several recurrence relations that govern the behaviour of these polynomials. Furthermore, we study specific cases to illustrate the applicability and versatility of this new class of polynomials.


  • 2-successive associated Stirling numbers
  • Exponential partial Bell polynomials
  • Generating function

2020 Mathematics Subject Classification

  • 05-XX
  • 05A18


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Manuscript history

  • Received: 21 September 2022
  • Revised: 26 April 2023
  • Accepted: 25 July 2023
  • Online First: 27 July 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Tiachachat, M., & Mihoubi, M. (2023). The 2-successive partial Bell polynomials. Notes on Number Theory and Discrete Mathematics, 29(3), 538-544, DOI: 10.7546/nntdm.2023.29.3.538-544.

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