StirlingS2[n, 7] == (1/720) (-1)^(n - 1) (-1 + n)! (HarmonicNumber[-1 + n]^6 - 15 HarmonicNumber[-1 + n]^4 HarmonicNumber[-1 + n, 2] + 40 HarmonicNumber[-1 + n]^3 HarmonicNumber[-1 + n, 3] + 45 HarmonicNumber[-1 + n]^2 (HarmonicNumber[-1 + n, 2]^2 - 2 HarmonicNumber[-1 + n, 4]) - 24 HarmonicNumber[-1 + n] (5 HarmonicNumber[-1 + n, 2] HarmonicNumber[-1 + n, 3] - 6 HarmonicNumber[-1 + n, 5]) + 5 (-3 HarmonicNumber[-1 + n, 2]^3 + 18 HarmonicNumber[-1 + n, 2] HarmonicNumber[-1 + n, 4] + 8 (HarmonicNumber[-1 + n, 3]^2 - 3 HarmonicNumber[-1 + n, 6]))) /; Element[n, Integers] && n > 0

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2007-05-02