\[\large\sum_{n=2}^{\infty}\frac{{e}^{-2n}}{{n}^{2}-1}\]

Consider the infinite sum above. If the solution can be expressed in the form \[\frac{1}{A}\left(1+\frac{{e}^{-B}}{C}\right)+\sinh{(D)}\ln{(1-{e}^{-E})}\]

find \(A\times B\times C\times D\times E. \)

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