  We use the ordinary Euler operator to compute the Ehrhart series for an
arbitrary lattice polytope. The resulting formula involves the coefficients of
the Ehrhart polynomial, combined via Eulerian numbers. We use this to compute
$h^*_{d-1}$ in terms of the coefficients of the Ehrhart polynomial, resulting
in a new linear inequality satisfied by the coefficents of the Ehrhart
polynomial.

Combinatorics