\[\displaystyle \sum_{n=1}^{\infty}{\frac{1}{P(2n,n)}} = \frac{{e}^{a}{\pi}^{b} \ \text{erf}(c)}{2}\]

Given the above summation with rational numbers \(a,b,c\) such that \(a + b + c = \frac{M}{G}\) for coprime positive integers, find \(M+G\)

**Details and Assumptions**

\(P(2n,n)\) is the permutation of \(2n\),\(n\)

\(\text{erf}(c)\) is the error function.

\(M\) and \(G\) are co-prime positive integers.

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