The problem is to evaluate the following sum over all permutations $\sigma\in S_{d}$ of $\{1,2,...,d\}$:

$\displaystyle\sum_{\sigma\in S_{d}}\text{sgn}(\sigma)\displaystyle\frac{1}{\prod_{i=1}^{d}(\sigma_{1} + \sigma_{2} + ... + \sigma_{i})}$.

This is similar to Question 1 here except the sign term. The conjecture is that our sum equals $\prod_{k=1}^{d-1}\frac{(k!)^{2}}{(2k+1)!}$. The problem and the conjecture arises from here.