  In 2018 Coll, Mayers, and Mayers conjectured that the $q$-series $( q, -q^3;
q^4 )_\infty^{-1}$ is the generating function for a certain parity statistic
related to the index of seaweed algebras. We prove this conjecture. Thanks to
earlier work by Seo and Yee, the conjecture would follow from the
non-negativity of the coefficients of this infinite product. Using a variant of
the circle method along with Euler-Maclaurin summation, we establish this
non-negativity, thereby confirming the Coll-Mayers-Mayers Conjecture.
