By analysis of moments of geometric distribution: New formulas involving Eulerian and Fubini numbers

The aim of this paper is to find new moment formulas for geometric distribution by using moments of the geometric distribution in terms of Apostol-type and Bernstein polynomials, and Fubini and Eulerian numbers, etc. A new generating function for moments of the geometric distribution is constructed. New sequences of special numbers with their recurrence relations are given. In order to compute values of these sequences and moments, codes in Wolfram language are given.