\[\large\displaystyle\sum_{n=1}^{\infty}\left({\displaystyle\sum_{k=0}^nk^2}\right)^{-1} \] If the value of the series above can be expressed as \(a-b\ln{(c)}\) where \(a,b\) are positive integers and \(c\) is the minimum possible positive integer, find the value of \(a+b+c\).

See Also Inverse Sum and Inverse Sum Cubed.

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