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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/04.14.03.0036.01









  


  










Input Form





StirlingS2[n, 10] == (1/362880) ((-1)^n (-1 + n)! (HarmonicNumber[-1 + n]^9 - 36 HarmonicNumber[-1 + n]^7 HarmonicNumber[-1 + n, 2] + 168 HarmonicNumber[-1 + n]^6 HarmonicNumber[-1 + n, 3] + 378 HarmonicNumber[-1 + n]^5 (HarmonicNumber[-1 + n, 2]^2 - 2 HarmonicNumber[-1 + n, 4]) - 504 HarmonicNumber[-1 + n]^4 (5 HarmonicNumber[-1 + n, 2] HarmonicNumber[-1 + n, 3] - 6 HarmonicNumber[-1 + n, 5]) - 420 HarmonicNumber[-1 + n]^3 (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]) + 216 HarmonicNumber[-1 + n]^2 (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]) + 63 HarmonicNumber[-1 + n] (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])) - 8 (315 HarmonicNumber[-1 + n, 2]^3 HarmonicNumber[-1 + n, 3] - 1134 HarmonicNumber[-1 + n, 2]^2 HarmonicNumber[-1 + n, 5] - 270 HarmonicNumber[-1 + n, 2] (7 HarmonicNumber[-1 + n, 3] HarmonicNumber[-1 + n, 4] - 12 HarmonicNumber[-1 + n, 7]) - 28 (10 HarmonicNumber[-1 + n, 3]^3 - 81 HarmonicNumber[-1 + n, 4] HarmonicNumber[-1 + n, 5] - 90 HarmonicNumber[-1 + n, 3] HarmonicNumber[-1 + n, 6] + 180 HarmonicNumber[-1 + n, 9])))) /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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</semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 6 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 3 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 216 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 35 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 84 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 70 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 120 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 7 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 63 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 180 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 160 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 6 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 32 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 8 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 315 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1134 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 270 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 7 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 28 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 90 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 6 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 81 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 180 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 9 </mn> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> StirlingS2 </ci> <ci> n </ci> <cn type='integer'> 10 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 362880 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <factorial /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 9 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 168 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 378 </cn> <apply> <plus /> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 504 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 420 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 216 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 70 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 120 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 63 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 180 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 160 </cn> <apply> <plus /> <apply> <power /> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> 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Date Added to functions.wolfram.com (modification date)





2007-05-02





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