Genocchi numbers and f-vectors of simplicial balls

The Genocchi numbers are the coefficients of the generating function 2tet+1. In this note we will give an equation for simplicial balls which involves these numbers. It relates the number of faces in the interior of the ball to the number of faces in the boundary of the ball. This is a variation of similar equations given in [P. McMullen, Triangulations of simplicial polytopes, Beiträge Algebra Geom. 45 (1) (2004) 37-46; S. Herrmann, M. Joswig, Bounds on the f-vectors of tight spans, Contrib. Discrete Math. (2006) (in press). arXiv:math.MG/0605401].