Factorial polynomials and associated number families

Alfred Schreiber
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 1, Pages 170–178
DOI: 10.7546/nntdm.2024.30.1.170-178
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Authors and affiliations

Alfred Schreiber
Department of Mathematics and Mathematical Education, University of Flensburg
Auf dem Campus 1, D-24943 Flensburg, Germany


Two doubly indexed families of polynomials in several indeterminates are considered. They are related to the falling and rising factorials in a similar way as the potential polynomials (introduced by L. Comtet) are related to the ordinary power function. We study the inversion relations valid for these factorial polynomials as well as the number families associated with them.


  • Potential polynomials
  • Faà di Bruno polynomials
  • Factorial polynomials
  • Inverse relations
  • Stirling numbers
  • Lah numbers

2020 Mathematics Subject Classification

  • 05A10
  • 11B65
  • 11B73
  • 11B83
  • 11C08


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Manuscript history

  • Received: 6 August 2023
  • Revised: 8 March 2024
  • Accepted: 12 March 2024
  • Online First: 13 March 2024

Copyright information

Ⓒ 2024 by the Author.
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

Schreiber, A. (2024). Factorial polynomials and associated number families. Notes on Number Theory and Discrete Mathematics, 30(1), 170-178, DOI: 10.7546/nntdm.2024.30.1.170-178.

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