Bernoulli-Padovan polynomials and Pado-Bernoulli matrices.

In the present work we introduce Bernoulli-Padovan numbers and polynomials. We give their generating functions of the Bernoulli-Padovan numbers and polynomials. We establish various relations involving the Bernoulli-Padovan numbers and polynomials by considering the Pado-derivative. We describe Pado-Bernoulli matrices in terms of the Bernoulli-Padovan numbers and polynomials. We establish a factorisation of the Pado-Bernoulli matrix by using a generalised Pado-Pascal matrix, and obtain the inverse of the Pado-Bernoulli matrix. Also, we give a relationship between the Pado-Bernoulli matrix and the Pado-Pascal matrix. [ABSTRACT FROM AUTHOR]