Andrews–Merca averaged truncation conjecture for Jacobi's triple product

Let $m,k,R,S$ be positive integers with $1\le S<R/2$. Consider the formal power series

$$\frac{(-1)^{k-1}}{(q^S,q^{R-S},q^{R};q^{R})_{\infty}} \sum_{0\le n<k}(-1)^nq^{\binom{n+1}{2}R-nS}(1-q^{(2n+1)S}).$$

Andrews–Merca's conjecture. The coefficient of $q^m$ in this series is non-negative.

This conjecture on averaged truncations of Jacobi's triple product identity was proved independently by Mao and Yee in 2015, with later combinatorial confirmation by He, Ji, and Zang and further proofs through different $q$-series identities.