  Motivated by my work on enumerative invariants for Quot schemes, I related
two power series obtained by two different means. One of them was computed
using geometric arguments via virtual localization methods and the other one
came from working with representation theoretic objects called vertex algebras.
In this note, I give proof of the equality of the two power series by relying
only on techniques related to Lagrange inversion. This makes my work on Quot
schemes independent of the previous results in the literature and proves a new
combinatorial identity.
