# Who's up to the challenge? 67

Calculus Level 5

$\large \sum _{ n=0 }^{ \infty }{ \dfrac { { 2 }^{ n+1 }n!^{ 2 } }{ (2n+1)!(n+1)^{ 2 } } } =A\pi G-\dfrac { B }{ C } \zeta (D)+\dfrac { { \pi }^{ E } }{ F } \ln { H }$

The equation above holds true for positive integers $$A,B,C,D,E,F$$ and $$H$$, where $$B,C$$ are coprime and $$H$$ is minimized.

Find $$A+B+C+D+E+F+H$$.

Notations:

• $$!$$ denotes the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.
• $$G$$ denotes the Catalan's constant, $$\displaystyle G = \sum_{n=0}^\infty \dfrac{ (-1)^n}{(2n+1)^2} \approx 0.916$$.
• $$\zeta(\cdot)$$ denotes the Riemann zeta function.
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