n!! == (n + 2)!!/(n + 2)

Cell[BoxData[RowBox[List[RowBox[List["n", "!!"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["n", "+", "2"]], ")"]], "!!"]], RowBox[List["n", "+", "2"]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> n </mi> <mo> !! </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> !! </mo> </mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Factorial2 </ci> <ci> n </ci> </apply> <apply> <times /> <apply> <ci> Factorial2 </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["n_", "!!"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["n", "+", "2"]], ")"]], "!!"]], RowBox[List["n", "+", "2"]]]]]]]

2001-10-29