Sur quelques propriétés de symétrie des nombres de Genocchi

Abstract

In [2] Dumont stated several conjectures about some symmetric polynomial sequences which are the refinements of the Genocchi numbers. In this paper we shall prove all of his conjectures. We first show that some special cases of his main conjecture can be readily derived from a result of Wall and then give a complete proof of this conjecture by computing some Hankel determinants. Finally, we present a new symmetric model for the Dumont-Foata polynomials in terms of Motzkin paths.