# Who's up to the challenge? 61

Calculus Level 5

$\sum _{ n=1 }^{ \infty }{ \frac { \Gamma \left( n+\frac { 1 }{ 2 } \right) }{ { n }^{ 2 }\Gamma (n) } } =A\sqrt [ B ]{ \pi } \ln { C }$

If the above equation holds true for positive integers $$A$$, $$B$$ and $$C$$, where $$C$$ is square-free, then find $$ABC$$.

Notation: $$\Gamma(\cdot)$$ denotes the Gamma function.

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