The Jack symmetric function Jλ(x;α) is a symmetric function with interesting properties that Jλ(x;2) is a spherical function of the symmetric pair (GL(n,), O(n,) and that Jλ(x;1) is the Schur function Sλ(x). Many interesting conjectures about the combinatorial properties of Jλ(x;α) are given by Stanley (1989). In this paper we give an affirmative answer to one of his conjectures.