  It is proved that a certain symmetric sequence of nonnegative integers
arising in the enumeration of magic squares of given size n by row sums or,
equivalently, in the generating function of the Ehrhart polynomial of the
polytope of doubly stochastic n by n matrices, is equal to the h-vector of a
simplicial polytope and hence that it satisfies the conditions of the
g-theorem. The unimodality of this sequance, which follows, was conjectured by
Stanley (1983). Several generalizations are given.
