  A ballot permutation is a permutation {\pi} such that in any prefix of {\pi}
the descent number is not more than the ascent number. In this article, we
obtained a formula in close form for the multivariate generating function of
{A(n,d,j)}, which denote the number of permutations of length n with d descents
and j as the first letter. Besides, by a series of calculations with
generatingfunctionology, we confirm a recent conjecture of Wang and Zhang for
ballot permutations.
