  Kerov considered the normalized characters of irreducible representations of
the symmetric group, evaluated on a cycle, as a polynomial in free cumulants.
Biane has proved that this polynomial has integer coefficients, and made
various conjectures. Recently, Sniady has proved Biane's conjectured explicit
form for the first family of nontrivial terms in this polynomial. In this
paper, we give an explicit expression for all terms in Kerov's character
polynomials. Our method is through Lagrange inversion.
