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I dont know how to proceed with solving $$\sum_{i=1}^{n}i^{k}(n+1-i).$$ Please give advise.

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    @RossMillikan In the summand, the power is a constant...2012-04-12
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    @DavidMitra: You are correct. It is not a duplicate.2012-04-12
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    First, find two generating functions for $n^k$ and $1+n$. Then product of them. Next, get the coefficient of $x^n$. You need the eulerian number for the generating function of the sequence $n^k$.2012-04-13

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