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\[ \large \sum_{n=1}^{\infty}\frac{H_{n}F_{n}}{2^{n}} = \ln(A) + \frac{B}{\sqrt{C}}\coth^{-1}\left (\frac{D}{\sqrt{E}} \right ) \] Find \[\large\frac{(A+B+C)^{2}}{DE}\]

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