  We study Quot schemes of 0-dimensional quotients of sheaves on 3-folds $X$.
When the sheaf $\mathcal{R}$ is rank 2 and reflexive, we prove that the
generating function of Euler characteristics of these Quot schemes is a power
of the MacMahon function times a polynomial. This polynomial is itself the
generating function of Euler characteristics of Quot schemes of a certain
0-dimensional sheaf, which is supported on the locus where $\mathcal{R}$ is not
locally free.
  In the case $X = \mathbb{C}^3$ and $\mathcal{R}$ is equivariant, we use our
result to prove an explicit product formula for the generating function. This
formula was first found using localization techniques in previous joint work
with B. Young. Our results follow from R. Hartshorne's Serre correspondence and
a rank 2 version of a Hall algebra calculation by J. Stoppa and R.P. Thomas.
