A class of polynomials and connections with Bernoulli's numbers

Motivated by certain problems connected with the stochastic analysis of the recursively defined time series, in this paper, we define and study some polynomial sequences. Beside computation of these polynomials and their connection to the Euler-Apostol numbers, we prove some basic properties and give an interesting connection of these polynomials with the well-known Bernoulli numbers, as well as some new summation formulas for Bernoulli's numbers. Finally, we prove that zeros of these polynomials are simple, real and symmetrically distributed in [0,1].