# Who's up to the challenge? 66

Calculus Level 5

$\large\sum _{ n=0 }^{ \infty }{ \dfrac { { L }_{ 2n+1 } }{ (2n+1)^{ 2 } \binom{2n}{n}} }$

Let $L_n$ denote the $n$th Lucas number, where $L_1 = 1$, $L_2 = 3$ and $L_n = L_{n-1} + L_{n-2}$ for $n \ge 3$.

If the series above can be expressed as $-\dfrac\pi A \ln\left( B - C\sqrt D+ E\sqrt{F - G\sqrt H} \right) + \dfrac IJ K ,$

where $A$, $B$, $C$, $D$, $E$, $F$, $H$, $I$ and $J$ are positive integers, with $I$ and $J$ being coprime integers; $D$, $E$ and $H$ square-free; and $K$ denotes the Catalan's constant, find $A+B+C+D+E+F+G+H+I+J$.

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