The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers
DOI:
https://doi.org/10.29020/nybg.ejpam.v12i3.3494Keywords:
$r$-Dowling numbers, $(r, \beta)$-Bell numbers, Bell polynomials, Lah numbers, $r$-Whitney numbers, Faa di Bruno's formula, $r$-Whitney-Lah numbersAbstract
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.Downloads
Published
2019-07-25
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How to Cite
The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers. (2019). European Journal of Pure and Applied Mathematics, 12(3), 1122-1137. https://doi.org/10.29020/nybg.ejpam.v12i3.3494