Complete and incomplete Bell polynomials associated with Lah-Bell numbers and polynomials

Abstract

The nth r-extended Lah-Bell number is defined as the number of ways a set with $n+r$ elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah-Bell polynomials and complete $r$-extended Lah-Bell polynomials respectively as multivariate versions of $r$-Lah numbers and the r-extended Lah-Bell numbers and to investigate some properties and identities for these polynomials. From these investigations, we obtain some expressions for the r-Lah numbers and the r-extended Lah-Bell numbers as finite sums.

10 pages

References in corpus (3)

• A Set of Identities for a Class of Alternating Binomial Sums Arising in Computing Applications
• Lah-Bell numbers and polynomials
• r-extended Lah-Bell numbers and polynomials associated with r-Lah numbers