This isn't as hard as it looks.

Algebra Level 3

[k=3n2(nk)]+(n+22)=4095\left[\sum_{k=3}^{n-2}\binom{n}{k}\right]+\binom{n+2}{2}=4095

If nn is a positive integer such that the above equation is true, then find the value of n22\frac{n^2}{2}.

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