Series involving factorials – mathoverflow.net

Playing around with this series for natural values of $a,b$, it appears that more generally for $c\in\mathbb N$, $$\sum_{k=0}^\infty \frac{ (a+k)! \ (b+k)!}{k!\ (a+b+c+1)! }=\frac{a!\ b!\ ...

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