  If the moments of a probability measure on $\R$ are interpreted as a
specialization of complete homogeneous symmetric functions, its free cumulants
are, up to sign, the corresponding specializations of a sequence of Schur
positive symmetric functions $(f_n)$. We prove that $(f_n)$ is the Frobenius
characteristic of the natural permutation representation of $\SG_n$ on the set
of prime parking functions. This observation leads us to the construction of a
Hopf algebra of parking functions, which we study in some detail.
