Explicit combinatorial interpretation of Kerov character polynomials as   numbers of permutation factorizations
  We find an explicit combinatorial interpretation of the coefficients of Kerov character polynomials which express the value of normalized irreducible characters of the symmetric groups S(n) in terms of free cumulants R_2,R_3,... of the corresponding Young diagram. Our interpretation is based on counting certain factorizations of a given permutation. 
Maciej Do{\l}ega, Valentin F\'eray, Piotr Sniady