Recurrence relation for instanton partition function in SU(N) gauge theory

We study the equivariant instanton partition function in $\mathcal{N}=2$ supersymmetric theory on ${\mathbb{C}}^2$ with $SU(N)$ gauge group and find the generalisation of the Zamolodchikov recurrence relation. We consider the pure theory as well as theories with matter hypermultiplets in the adjoint and fundamental representations.