Sur une extension des nombres de Genocchi

Abstract

We study the sequence of polynomials B n ( x, y) defined through the recurrence B 1( x, y) = 1, B n ( x, y) = ( x + 1)( y + 1) B n−1 ( x + 1, y + 1) − xyB n−1 ( x, y), which extend the Gandhi polynomials generating the Genocchi numbers. We give a combinatorial interpretation of these polynomials, and a continued fraction representation for their ordinary generating function.