Series involving reciprocal of the central binomial coefficient squared


        Today we will prove this infinite series which involves the reciprocal of the central binomial coefficient squared, namely


\begin{align*}
\sum_{n=1}^\infty\frac{ 2^{4n}}{n^3 \binom{2n}{n}^2}&=8\pi\beta(2)-14\zeta(3)
\end{align*}


Click here for the proof.

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