Identities and Relations Containing Finite Sums of Powers of Binomial Coefficients.

The purpose of this paper is to study and give some identities and relations related to the families of the numbers and polynomials, arising from finite sums involving higher powers of binomial coefficients, which were recently introduced in [7]. By applying p-adic integrals to these finite sums, we derive some new combinatorial sums involving not only these numbers and polynomials, but also the Bernoulli numbers and polynomials, and the Euler numbers and polynomials. [ABSTRACT FROM AUTHOR]