StirlingS1[m + 7, m] == (-(Pochhammer[m, 8]/5806080)) (6 + m) (7 + m) (6008 + 5182 m + 1563 m^2 + 198 m^3 + 9 m^4) /; Element[m, Integers] && m >= 0

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <semantics> <mi> S </mi> <annotation encoding='Mathematica'> TagBox[&quot;S&quot;, StirlingS1] </annotation> </semantics> <mrow> <mi> m </mi> <mo> + </mo> <mn> 7 </mn> </mrow> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </msubsup> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mn> 8 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;m&quot;, &quot;)&quot;]], &quot;8&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 198 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1563 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5182 </mn> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mn> 6008 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 5806080 </mn> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> StirlingS1 </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> 7 </cn> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> m </ci> <cn type='integer'> 8 </cn> </apply> <apply> <plus /> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <ci> m </ci> <cn type='integer'> 7 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 198 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1563 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5182 </cn> <ci> m </ci> </apply> <cn type='integer'> 6008 </cn> </apply> <apply> <power /> <cn type='integer'> 5806080 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02