On the Translated Whitney Numbers and their Combinatorial Properties
Mahid M. Mangontarum *
Department of Mathematics, Mindanao State University-Main Campus, Marawi City, Philippines 9700, Philippines.
Amerah M. Dibagulun
Department of Mathematics, Mindanao State University-Main Campus, Marawi City, Philippines 9700, Philippines.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we further develop the study of the translated Whitney numbers by deriving more combinatorial properties such as more recurrence relations, exponential and rational generating functions and the orthogonality and inverse relations. To achieve this goal, we introduce the “signed” translated Whitney numbers of the first kind. A relationship between these numbers and the Bernoulli polynomials is also briefly discussed.
Keywords: Translated whitney numbers, whitney numbers, stirling numbers