Series Demystified 3

Algebra Level 4

\[ \large \sum_{n=1}^{48} \left [ \frac {n!(n^2+n-1)}{n\sqrt{n+1}+\sqrt n}\right] \]

If the summation above equals to \(S\), find the value of \( \frac{S+1}{48!} \).

This is one of my original Series Demystified problems.
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