English

r-extended Lah-Bell numbers and polynomials associated with r-Lah numbers

Number Theory 2020-08-17 v1

Abstract

The aim of this paper is to study some basic properties of the r$-extended Lah-Bell numbers and polynomials associated with r-Lah numbers and to show the connection between the r-extended Lah-Bell polynomials and the rising factorial moments of the Poisson random variable shifted by an even nonnegative integer 2r. Here the nth r-extended Lah-Bell number counts the number of ways a set of n+r elements can be partitioned into non-empty linearly ordered subsets such that r distinguished elements have to be in distinct linearly ordered subsets and the r-extended Lah-Bell polynomials are natural extensions of the r-extended Lah-Bell numbers.

Keywords

Cite

@article{arxiv.2008.06155,
  title  = {r-extended Lah-Bell numbers and polynomials associated with r-Lah numbers},
  author = {Dae San Kim and Taekyun Kim},
  journal= {arXiv preprint arXiv:2008.06155},
  year   = {2020}
}

Comments

10 pages