# Inspired by Patrick Corn

Calculus Level 5

Let $${ H }_{ n }^{ (2) }=\displaystyle\sum _{ k=1 }^{ n }{ \dfrac { 1 }{ { k }^{ 2 } } }$$, and if $\sum _{ n=1 }^{ \infty }{ \dfrac { { H }_{ n }^{ (2) } }{ { 2 }^{ n } } }$

is in the form $\dfrac { { \pi }^{ a } }{ b } -(\ln d)^c,$

where $$a,b,c$$ and $$d$$ are integers, find $$a+b+c+d$$.

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