Contents

Online Journal of Analytic Combinatorics

  • Research article

Six proofs for an identity of the Lah numbers

Bai-Ni Guo1, Feng Qi2
1COLLEGE OF MATHEMATICS, INNER MONGOLIA UNIVERSITY FOR NATIONALITIES, TONGLIAO CITY, INNER MONGOLIA AUTONOMOUS REGION, 028043, CHINA;
2DEPARTMENT OF MATHEMATICS, COLLEGE OF SCIENCE, TIANJIN POLYTECHNIC UNIVERSITY, TIANJIN CITY, 300387, CHINA
  • Published: 31/12/2015

Abstract

In the paper, utilizing respectively the induction, a generating function of the Lah numbers, the Chu-Vandermonde summation formula, an inversion formula, the Gauss hypergeometric series, and two generating functions of Stirling numbers of the first kind, the authors collect and provide six proofs for an identity of the Lah numbers.

Keywords: proof; identity; Lah number; induction; falling factorial; Stirling numbers of the first kind; generating function; derivative formula; exponential function; Chu-Vandermonde summation formula; inversion formula; Gauss hypergeometric series.
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Citation
Bai-Ni Guo, Feng Qi. Six proofs for an identity of the Lah numbers[J], Online Journal of Analytic Combinatorics, Issue 10, 2015. -. DOI: .