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 BellB

 http://functions.wolfram.com/04.23.06.0002.01

 Input Form

 BellB[n] == Ceiling[(1/E) Sum[k^n/k!, {k, 1, 2 n}]] /; Element[n, Integers] && n > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BellB", "[", "n", "]"]], "\[Equal]", RowBox[List["Ceiling", "[", RowBox[List[FractionBox["1", "\[ExponentialE]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["2", "n"]]], " ", FractionBox[SuperscriptBox["k", "n"], RowBox[List["k", "!"]]]]]]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]

 MathML Form

 B TagBox["B", BellB] n 1 k = 1 2 n k n k ! /; n + TagBox[SuperscriptBox["\[DoubleStruckCapitalN]", "+"], Function[Integers]] Condition BellB n 1 -1 k 1 2 n k n k -1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BellB", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Ceiling", "[", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["2", " ", "n"]]], FractionBox[SuperscriptBox["k", "n"], RowBox[List["k", "!"]]]]], "\[ExponentialE]"], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]

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

 2007-05-02