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Article

Summation Formulas for Certain Combinatorial Sequences

1
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
2
School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(8), 1210; https://doi.org/10.3390/math12081210
Submission received: 21 February 2024 / Revised: 16 April 2024 / Accepted: 16 April 2024 / Published: 17 April 2024

Abstract

In this work, we establish some characteristics for a sequence, Aα(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 Aα(n,k) and r-Whitney–Lah numbers is established, and some formulas for the r-Whitney–Lah numbers are obtained.
Keywords: Lah numbers; Stirling numbers of the first kind; multiple harmonic numbers; Cauchy numbers; Catalan numbers Lah numbers; Stirling numbers of the first kind; multiple harmonic numbers; Cauchy numbers; Catalan numbers

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MDPI and ACS Style

Chen, Y.; Guo, D. Summation Formulas for Certain Combinatorial Sequences. Mathematics 2024, 12, 1210. https://doi.org/10.3390/math12081210

AMA Style

Chen Y, Guo D. Summation Formulas for Certain Combinatorial Sequences. Mathematics. 2024; 12(8):1210. https://doi.org/10.3390/math12081210

Chicago/Turabian Style

Chen, Yulei, and Dongwei Guo. 2024. "Summation Formulas for Certain Combinatorial Sequences" Mathematics 12, no. 8: 1210. https://doi.org/10.3390/math12081210

APA Style

Chen, Y., & Guo, D. (2024). Summation Formulas for Certain Combinatorial Sequences. Mathematics, 12(8), 1210. https://doi.org/10.3390/math12081210

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