Generating function for reverse plane partitions

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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