  The superconformal index for N=2 5d theories contains a non-perturbative part
arising from 5d instantonic operators which coincides with the Nekrasov
instanton partition function. In this note, for pure gauge theories, we
elaborate on the relation between such instanton index and the Hilbert series
of the instanton moduli space. We propose a non-trivial identification of
fugacities allowing the computation of the instanton index through the Hilbert
series. We show the agreement of our proposal with existing results in the
literature, as well as use it to compute the exact index for a pure U(1) gauge
theory.
