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Let $n \in N$ and $q\geq 2$.

I am trying to calculate the following sum: $ \sum_{i=0}^{\sqrt n/2}\sum_{j= i \sqrt n }^{(i+1)\sqrt n}\frac{(-1)^q2^q(\frac{n}{2}-j)^q}{(n-j)!j!} $

Any help will be appreciated.

Thank you.

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    @ Vadim: thank you. Vadim, could you please elaborate-why we dont need summation over i in the first case. And also, how to calcukate the obtained sum? Thank you very much.2012-04-17

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