Open AccessThe r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers
Author(s) -
Roberto B. Corcino,
Charles B. Montero,
Maribeth B. Montero,
Jay M. Ontolan
Publication year - 2019
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v12i3.3494
Subject(s) - mathematics , combinatorics , identity (music) , product (mathematics) , bell polynomials , pure mathematics , discrete mathematics , physics , geometry , acoustics
This paper derives another form of explicit formula for $(r,\beta)$-Bell numbers using the Faa di Bruno's formula and certain identity of Bell polynomials of the second kind. This formula is expressed in terms  of the $r$-Whitney numbers of the second kind and the ordinary Lah numbers. As a consequence, a relation between $(r,\beta)$-Bell numbers and the sums of row entries of the product of two matrices containing the $r$-Whitney numbers of the second kind and the ordinary Lah numbers is established.  Moreover, a $q$-analogue of the explicit formula is obtained.