A Generalization of Stirling, Lah, and Harmonic Numbers with Some Computational Applications

Abstract

In this article, we give a generalization of the multiparameter non-central Stirling numbers of the first and second kinds, Lah numbers, and harmonic numbers. Some new combinatorial identities, new explicit formulas, and many relations between different types of Stirling numbers and generalized harmonic numbers are found. Moreover, some interesting special cases of the generalized multiparameter non-central Stirling numbers are deduced. Furthermore, a matrix representation of the results obtained is given and a computer program is written using Maple and executed for calculating \(GMPNSN-1\) and their inverse \((GMPNSN-2)\), along with some of their interesting special cases.