New approach of Bernoulli and Genocchi Numbers and their associated polynomials, via generalized Fibonacci sequences of order

Abstract

We are interested here in the application of 1-generalized Fibonacci sequences (1-GFS for short), to study some properties of Bernoulli and Genocchi numbers and their related classical numbers and polynomials. That is, properties of this class of sequences, allows us to derive new recursive relations for generating Bernoulli and Genocchi numbers, and their related polynomials.