It is simpler than it looks!

Calculus Level 5

\[\sum _{ n=1 }^{ \infty }{ \frac { 1 }{ { n }^{ 2 }\left( \begin{matrix} 2n \\ n \end{matrix} \right) } } =\frac { A }{ B } \zeta \left( C \right) \]

In the equation above, \(A,B,C\) are positive integers such that \(A\) and \(B\) are co-prime.

Find \(A+B+C.\)

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