A q-Analogue of Qi Formula for r-Dowling numbers
Commun. Korean Math. Soc.
Published online July 1, 2019
Joy Antonette D. Cillar and Roberto B. Corcino
University of San Jose- Recoletos, Cebu Normal University
Abstract : In this paper, we establish an explicit formula for $r$-Dowling numbers in terms of $r$-Whitney Lah and $r$-Whitney numbers of the second kind. This is a generalization of the Qi formula for Bell numbers in terms of Lah and Stirling numbers of the second kind. Moreover, we define the $q,r$-Dowling numbers, $q,r$-Whitney Lah numbers and $q,r$-Whitney numbers of the first kind and obtain several fundamental properties of these numbers such as orthogonality and inverse relations, recurrence relations, and generating functions. Hence, we derive an analogous Qi formula for $q,r$-Dowling numbers expressed in terms of $q,r$-Whitney Lah numbers and $q,r$-Whitney numbers of the second kind.
Keywords : r-Dowling numbers, r-Whitney numbers, Lah numbers, recurrence relation, explicit formula, generating function, q-analogue
MSC numbers : 05A10, 05A15, 11B65, 11B73
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