We derive an expression for generating function of irreducible character of $\mathfrak{S}_n$ corresponding to two row partition $(n-k, k)$ and hook partition $(n-k, 1^k)$ in terms of cycle statistics of evaluating permutation. We use Doubilet inversion formula \cite{doubilet} and homology of poset of tilings for our derivation. As an application we give a new proof of M. Rosas formula \cite{rosas} for Kronecker coefficients of two row partition and hook partition.