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http://functions.wolfram.com/06.41.08.0001.01
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CatalanNumber[z] == (2/(z + 1)!) Product[4 k + 2, {k, 1, z - 1}]
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Cell[BoxData[RowBox[List[RowBox[List["CatalanNumber", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["2", RowBox[List[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], "!"]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], RowBox[List["z", "-", "1"]]], RowBox[List["(", RowBox[List[RowBox[List["4", " ", "k"]], "+", "2"]], ")"]]]]]]]]]]
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<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["C", CatalanNumber] </annotation> </semantics> <mi> z </mi> </msub> <mo>  </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mtext> </mtext> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> CatalanNumber </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["CatalanNumber", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], RowBox[List["z", "-", "1"]]], RowBox[List["(", RowBox[List[RowBox[List["4", " ", "k"]], "+", "2"]], ")"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], "!"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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