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http://functions.wolfram.com/04.15.03.0003.02
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StirlingS2[n, 2] == 2^(n - 1) - 1 + (1/2) KroneckerDelta[n] /;
Element[n, Integers] && n >= 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["StirlingS2", "[", RowBox[List["n", ",", "2"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List["n", "-", "1"]]], "-", "1", "+", RowBox[List[FractionBox["1", "2"], RowBox[List["KroneckerDelta", "[", "n", "]"]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "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["\[ScriptCapitalS]", StirlingS2] </annotation> </semantics> <mi> n </mi> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ⩵ </mo> <mrow> <mfrac> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mi> n </mi> </msub> <mn> 2 </mn> </mfrac> <mo> + </mo> <msup> <mn> 2 </mn> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> StirlingS2 </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> KroneckerDelta </ci> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StirlingS2", "[", RowBox[List["n_", ",", "2"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["n", "-", "1"]]], "-", "1", "+", FractionBox[RowBox[List["KroneckerDelta", "[", "n", "]"]], "2"]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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