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 Factorial2

 http://functions.wolfram.com/06.02.16.0005.01

 Input Form

 (-2 n - 1)!! == (-1)^n/(2 n - 1)!! /; Element[n, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], "n"]], "-", "1"]], ")"]], "!!"]], "\[Equal]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]], ")"]], "!!"]]]]], " ", "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

 MathML Form

 ( - 2 n - 1 ) !! ( - 1 ) n ( 2 n - 1 ) !! /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition Factorial2 -2 n -1 -1 n Factorial2 2 n -1 -1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "n_"]], "-", "1"]], ")"]], "!!"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]], ")"]], "!!"]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

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

 2001-10-29