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Calculus Level 5

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

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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