AIMS Mathematics (Jan 2022)

Note on r-central Lah numbers and r-central Lah-Bell numbers

  • Hye Kyung Kim

DOI
https://doi.org/10.3934/math.2022161
Journal volume & issue
Vol. 7, no. 2
pp. 2929 – 2939

Abstract

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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.

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