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$\large \sum_{n=1}^\infty \frac{1}{{2n \choose n}}$

Suppose the following infinite sum can be written as $\dfrac{a+\pi b\sqrt{c}}{d},$

where $a,b,c$ and $d$ are integers with $b$ and $c$ prime. Then compute the value of $a+b+c+d$,

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