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CatalanNumber




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CatalanNumber[n] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/06.41.27.0001.01









  


  








Input Form





CatalanNumber[z] == Binomial[2 z, z]/(z + 1)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["CatalanNumber", "[", "z", "]"]], "\[Equal]", FractionBox[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", "z"]], ",", "z"]], "]"]], RowBox[List["z", "+", "1"]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msub> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox[&quot;C&quot;, CatalanNumber] </annotation> </semantics> <mi> z </mi> </msub> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> z </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;z&quot;]], Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[&quot;z&quot;, Identity, Rule[Editable, True], Rule[Selectable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> CatalanNumber </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Binomial </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["CatalanNumber", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "z"]], ",", "z"]], "]"]], RowBox[List["z", "+", "1"]]]]]]]


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





2007-05-02