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StirlingS1






Mathematica Notation

Traditional Notation









Integer Functions > StirlingS1[n,m] > Specific values > Specialized values > For fixed n





http://functions.wolfram.com/04.14.03.0035.01









  


  










Input Form





StirlingS2[n, 9] == (1/40320) ((-1)^(n - 1) (-1 + n)! (HarmonicNumber[-1 + n]^8 - 28 HarmonicNumber[-1 + n]^6 HarmonicNumber[-1 + n, 2] + 112 HarmonicNumber[-1 + n]^5 HarmonicNumber[-1 + n, 3] + 210 HarmonicNumber[-1 + n]^4 (HarmonicNumber[-1 + n, 2]^2 - 2 HarmonicNumber[-1 + n, 4]) - 224 HarmonicNumber[-1 + n]^3 (5 HarmonicNumber[-1 + n, 2] HarmonicNumber[-1 + n, 3] - 6 HarmonicNumber[-1 + n, 5]) - 140 HarmonicNumber[-1 + n]^2 (3 HarmonicNumber[-1 + n, 2]^3 - 8 HarmonicNumber[-1 + n, 3]^2 - 18 HarmonicNumber[-1 + n, 2] HarmonicNumber[-1 + n, 4] + 24 HarmonicNumber[-1 + n, 6]) + 48 HarmonicNumber[-1 + n] (35 HarmonicNumber[-1 + n, 2]^2 HarmonicNumber[-1 + n, 3] - 70 HarmonicNumber[-1 + n, 3] HarmonicNumber[-1 + n, 4] - 84 HarmonicNumber[-1 + n, 2] HarmonicNumber[-1 + n, 5] + 120 HarmonicNumber[-1 + n, 7]) + 7 (15 HarmonicNumber[-1 + n, 2]^4 - 180 HarmonicNumber[-1 + n, 2]^2 HarmonicNumber[-1 + n, 4] - 160 HarmonicNumber[-1 + n, 2] (HarmonicNumber[-1 + n, 3]^2 - 3 HarmonicNumber[-1 + n, 6]) + 12 (15 HarmonicNumber[-1 + n, 4]^2 + 32 HarmonicNumber[-1 + n, 3] HarmonicNumber[-1 + n, 5] - 60 HarmonicNumber[-1 + n, 8])))) /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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