# Bino Harmonic Series 2

Calculus Level 5

$\text{S} = \displaystyle \sum_{n=0}^\infty \left[\binom{2n}{n}^2\frac{ H_n}{2^{5n}} \right]$

$$\text{S}$$ can be represented as

$\dfrac{\sqrt{\pi^{\text{A}}}}{\text{B} \ \Gamma^2\left(\frac{\text{C}}{\text{D}} \right)}(\text{E}\pi - \text{F}\log \text{G})$

where $$\text{A}, \text{B}, \text{C}, \text{D}, \text{E}, \text{F}$$ and $$\text{G}$$ are positive integers, $$\gcd (\text{C},\text{D}) = \gcd(\text{B},\text{E}) = 1$$ and $$\text{G}$$ is a prime number.

Evaluate $$\text{A}+\text{B}+\text{C}+\text{D}+\text{E}+\text{F}+\text{G}$$