Combinatorial Identities and Sums for Special Numbers and Polynomials

Abstract

In this paper, by using some families of special numbers and polynomials
with their generating functions and functional equations, we derive many new identities and relations related these numbers and polynomials. These results associated with the well-known numbers and polynomials such as the Euler numbers, Stirling numbers of the second kind, central factorial numbers and array polynomials. Furthermore, by using higher-order partial differential equations, we also derive some combinatorial sums and identities. Finally, we give two computation algorithms for the Euler numbers and the central factorial numbers.