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Summation Formulas for Certain Combinatorial Sequences

Author

Listed:
  • Yulei Chen

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China)

  • Dongwei Guo

    (School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China)

Abstract

In this work, we establish some characteristics for a sequence, A α ( n , k ) , including recurrence relations, generating function and inversion formula, etc. Based on the sequence, we derive, by means of the generating function approach, some transformation formulas concerning certain combinatorial numbers named after Lah, Stirling, harmonic, Cauchy and Catalan, as well as several closed finite sums. In addition, the relationship between A α ( n , k ) and r -Whitney–Lah numbers is established, and some formulas for the r -Whitney–Lah numbers are obtained.

Suggested Citation

  • Yulei Chen & Dongwei Guo, 2024. "Summation Formulas for Certain Combinatorial Sequences," Mathematics, MDPI, vol. 12(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1210-:d:1377634
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