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Subfactorial




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Subfactorial[n] > Specific values > Specialized values





http://functions.wolfram.com/06.42.03.0002.01









  


  








Input Form





Subfactorial[n] == Round[n!/E] /; Element[n, Integers] && n > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Subfactorial", "[", "n", "]"]], "\[Equal]", RowBox[List["Round", "[", " ", FractionBox[RowBox[List["n", "!"]], "\[ExponentialE]"], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> Subfactorial </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mi> &#8519; </mi> </mfrac> <mo> &#8969; </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[List[], Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mi> Subfactorial </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mi> &#8519; </mi> </mfrac> <mo> &#8969; </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[List[], Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Subfactorial", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Round", "[", FractionBox[RowBox[List["n", "!"]], "\[ExponentialE]"], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]


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





2007-05-02