Skip to main content
SpringerLink
Log in

A Combinatorial Approach to the Generalized Central Factorial Numbers

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In the present article, we make use of the set partitions and the generating functions to give new combinatorial relations for the generalized central factorial numbers. In the second part of the paper, we present a relationship between the Bernoulli polynomials and the Stirling numbers with higher level.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Broder, A.Z.: The \(r\)-Stirling numbers. Discrete Math. 49, 241–259 (1984)

    Article  MathSciNet  Google Scholar 

  2. Butzer, P.L., Schimidt, M., Stark, E.L., Vogt, L.: Central factorial numbers; their main properties and some applications. Numer. Funct. Anal. Optimiz. 10, 419–488 (1989)

    Article  MathSciNet  Google Scholar 

  3. Carlitz, L., Riordan, J.: The divided central differences of zero. Can. J. Math. 15, 94–100 (1963)

    Article  MathSciNet  Google Scholar 

  4. Domaratzki, M.: Combinatorial interpretations of a generalization of the Genocchi numbers. J. Integer Seq. 7, 5 (2004). (Article 04.3.6)

    MathSciNet  MATH  Google Scholar 

  5. Dumont, D.: Interpretations combinatoires des nombres de Genocchi. Duke Math. J. 41, 305–318 (1974)

    Article  MathSciNet  Google Scholar 

  6. Foata, D., Han, G.-N.: Principes de Combinatoire Classique. Lecture Notes, Strasbourg (2000)

  7. Komatsu, T., Ramírez, J.L., Villamizar, D.: A combinatorial approach to the Stirling numbers of the first kind with higher level. Studia Sci. Math. Hungar. (2021)

  8. Mansour, T.: Combinatorics of Set Partitions. CRC Press, Boca Raton (2012)

    Book  Google Scholar 

  9. Merca, M.: Connections between central factorial numbers and Bernoulli numbers. Period. Math. Hung. 73, 259–264 (2016)

    Article  MathSciNet  Google Scholar 

  10. Mező, I.: Combinatorics and Number Theory of Counting Sequences. CRC Press, Boca Raton (2019)

    Book  Google Scholar 

  11. Riordan, J.: Combinatorial Identities. Wiley, Hoboken (1968)

    MATH  Google Scholar 

  12. Tweedie, C.: The Stirling numbers and polynomials. Proc. Edinburgh Math. Soc. 37, 2–25 (1918)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Takao Komatsu

  2. Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia

    José L. Ramírez

  3. Department of Mathematics and Systems Analysis, Aalto University, 00076, Aalto, Finland

    Diego Villamizar

Authors
  1. Takao Komatsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José L. Ramírez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Diego Villamizar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José L. Ramírez.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Komatsu, T., Ramírez, J.L. & Villamizar, D. A Combinatorial Approach to the Generalized Central Factorial Numbers. Mediterr. J. Math. 18, 192 (2021). https://doi.org/10.1007/s00009-021-01830-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-021-01830-5

Keywords

Mathematics Subject Classification

Search

Navigation