@article{Kim2022, 
author = {Hye Kyung Kim},
title = {Note on    r-central Lah numbers and    r-central Lah-Bell numbers},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {2},
pages = {2929-2939},
keywords = {Lah numbers, Lah-Bell numbers, r-Lah numbers, r-Lah-Bell polynomials, central factorial numbers of the second kind},
url = {https://www.sciopen.com/article/10.3934/math.2022161},
doi = {10.3934/math.2022161},
abstract = {The    r-Lah numbers generalize the Lah numbers to the    r-Stirling numbers in the same sense. The Stirling numbers and the central factorial numbers are one of the important tools in enumerative combinatorics. The    r-Lah number counts the number of partitions of a set with    n  +  r elements into    k  +  r ordered blocks such that    r distinguished elements have to be in distinct ordered blocks. In this paper, the    r-central Lah numbers and the    r-central Lah-Bell numbers (   r  ∈      N  ) are introduced parallel to the    r-extended central factorial numbers of the second kind and    r-extended central Bell polynomials. In addition, some identities related to these numbers including the generating functions, explicit formulas, binomial convolutions are derived. Moreover, the    r-central Lah numbers and the    r-central Lah-Bell numbers are shown to be represented by Riemann integral, respectively.}
}