Combinatorial applications of the special numbers and polynomials

Abstract

In this paper, by using some families of special numbers and polynomials with their generating functions, we give various properties of these numbers and polynomials. These numbers are related to the well-known numbers and polynomials, which are the Euler numbers, the Stirling numbers of the second kind, the central factorial numbers and the array polynomials. We also discuss some combinatorial interpretations of these numbers related to the rook polynomials and numbers. Furthermore, we give computation formulas for these numbers and polynomials.

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References in corpus (1)

• New families of special numbers for computing negative order Euler numbers

Cited by in corpus (3)

• New integral formulas and identities involving special numbers and functions derived from certain class of special combinatorial sums
• Derivation of Computational Formulas for certain class of finite sums: Approach to Generating functions arising from $p$-adic integrals and special functions
• Construction of a generalization of the Leibnitz numbers and their properties