The MacMahon function is a generating function over total boxes $n=|\pi|$ for the total number $p_n$ of 3d plane partitions $\pi$:
$$ \prod_{k=1}^{\infty} \frac{1}{(1-x^k)^k} = \sum_{n}p_n x^n$$
Is there an analogous formula for reverse plane partitions. I'm aware of the hook formula:
$$ \sum_{\pi \in \text{RPP}(\lambda)} x^{|\pi|} = \prod_{s \in \lambda} \frac{1}{1-x^{h_{\lambda}(s)}} $$
But I'm wondering if there exists a generating function that doesn't fix the base!
Thanks