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 EulerE

 http://functions.wolfram.com/04.12.23.0001.01

 Input Form

 Sum[Binomial[2 n, 2 k] EulerE[2 k], {k, 0, n}] == 0 /; Element[n, Integers] && n > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "n"]], ",", RowBox[List["2", " ", "k"]]]], "]"]], " ", RowBox[List["EulerE", "[", RowBox[List["2", " ", "k"]], "]"]]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]

 MathML Form

 k = 0 n ( 2 n 2 k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["2", " ", "n"]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List["2", " ", "k"]], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] E TagBox["E", EulerE] 2 k 0 /; n + TagBox[SuperscriptBox["\[DoubleStruckCapitalN]", "+"], Function[Integers]] Condition k 0 n Binomial 2 n 2 k EulerE 2 k 0 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "n_"], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["2", " ", "n_"]], ",", RowBox[List["2", " ", "k_"]]]], "]"]], " ", RowBox[List["EulerE", "[", RowBox[List["2", " ", "k_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]

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

 2001-10-29