The superconformal index for N=2* U(N) theories are computed using the formulation by Iqbal&Vafa from the refined topological string partition functions. By the fiber-base duality this class of theories are related to U(1) quiver theories with fundamental and bi-fundamentel matter. The partition function for N=2* theory is argued to compute the elliptic genus for the bundle over the instanton moduli space of the quiver theory.
