Sum[k^i (n - k)^j, {k, 0, n}] == ((i! j!) n^(i + j + 1))/(i + j + 1)! + (1/2) n^(i + j) (KroneckerDelta[i j, 0] + KroneckerDelta[i + j, 0]) + Sum[(1/k) (KroneckerDelta[Mod[k, 2], 0] BernoulliB[k] ((-1)^j Binomial[i, i + j + 1 - k] + (-1)^i Binomial[j, i + j + 1 - k]) n^(i + j + 1 - k)), {k, 1 + Min[i, j], i + j}] /; Element[n, Integers] && n >= 0 && Element[i, Integers] && i >= 0 && Element[j, Integers] && j >= 0

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</ci> </apply> <apply> <in /> <ci> j </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2002-12-18