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Evalute triple sum $ \sum_{m\geq 0}\sum_{n \geq 0}\sum_{p\geq 0} \frac{m!n!p!}{(m+n+p+2)!}$
I had a triple $T$ sum to evaluate
$$\sum_{m\geq 0}\sum_{n \geq 0}\sum_{p\geq 0} \frac{m!n!p!}{(m+n+p+2)!}$$ where $!$ denotes factorials.
The managed to find the closed form of it, $\displaystyle \...
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