Quasi symmetric plane partitions enumeration conjecture

Let $\operatorname{qspp}(a,c)$ denote the number of quasi symmetric plane partitions inside an $(a,a,c)$-box. Let $p_a(c)$ be a polynomial in $\mathbb{Q}[c]$. Quasi symmetric plane partitions conjecture.

$$\operatorname{qspp}(a,c-a)=\begin{cases} c\binom{c+a-1}{2a-1}p_a(c)&a\text{ is even},\\ \binom{c+a-1}{2a-1}p_a(c)&a\text{ is odd}, \end{cases}$$

Here $p_a(c)$ is irreducible and even, meaning $p_a(c)=p_a(-c)$, and the common denominator of its coefficients is a product of “small primes”. This is one of three conjectural enumeration formulas obtained from computer experiments; the claimed formulas are supported by data for small parameter values.