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$$(nm-k)![\frac{x^{k-1}}{(k-1)!}]\prod_{d\in \{n,m\}}\mathcal{B}[(\sum^d_{j\in odd}\frac{\frac{2}{d+1}\cot^2(\frac{\pi j}{2(d+1)})}{1-2\cos(\frac{\pi j}{d+1})x})]$$
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