A NOTE ON GENERALIZED NARAYANA SEQUENCE

Résumé

The purpose of this article is to present a new sequence of numbers using the concept binomial coefficient. This new sequence is a generalization of Narayana’s numbers. From this definition we will establish some properties, we will prove some identities and establish connections between this new sequence and the Catalan numbers. Finally, the generalized Narayana central numbers are defined and for some special cases, such as r = 1, 2, 3 and 4, identities involving the generalized Narayana central
numbers and Catalan numbers are given and thus we establish a formula for the central Narayana numbers in terms of the Catalan numbers.