Only if this could be "Series Demystified 8"

Algebra Level 5

n=148n2+n1(n+2)!\large \displaystyle \sum_{n=1}^{48} \dfrac{n^2 + n - 1}{(n+2)!}

If the above summation equals to SS, find 50!(12S)50!\left(\dfrac{1}{2} - S \right).

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