Summation Formulas for Certain Combinatorial Sequences

Yulei Chen and Dongwei Guo ()
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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

Mathematics, 2024, vol. 12, issue 8, 1-16

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.

Keywords: Lah numbers; Stirling numbers of the first kind; multiple harmonic numbers; Cauchy numbers; Catalan numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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