What is the value of this double sum in closed form? – mathoverflow.net

What is the value of this double sum in closed form? – mathoverflow.net

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I encountered the following double sum which requires an evaluation. Is there a closed form for this? $$\sum_{n=0}^{\infty}\frac{\sum_{k=0}^n\binom{n}k^{-1}}{(n+1)(n+2)}.$$ Incidentally, it ...

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