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 Catalan

 http://functions.wolfram.com/02.07.06.0004.01

 Input Form

 Catalan == (1/2) Sum[(4^k k!^2)/((2 k)! (2 k + 1)^2), {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List["Catalan", "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["4", "k"], " ", SuperscriptBox[RowBox[List["k", "!"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", " ", "k"]], ")"]], "!"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "2"]]]]]]]]]]]]

 MathML Form

 C TagBox["C", Function[Catalan]] 1 2 k = 0 4 k k ! 2 ( 2 k ) ! ( 2 k + 1 ) 2 Catalan 1 2 k 0 4 k k 2 2 k 2 k 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "Catalan", "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["4", "k"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["k", "!"]], ")"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", " ", "k"]], ")"]], "!"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "2"]]]]]]]]]]]]

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

 2001-10-29