On Composition of Generating Functions

In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvement of the composita formulae’s given in [7, 3]. Using the new composita formula’s, we construct a variety of combinatorics identities. This study go alone to define new family of generalized Bernoulli polynomials which include Hermite-Bernoulli polynomials introduced by Dattoli and al [1].