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 BellB

 http://functions.wolfram.com/04.23.17.0001.01

 Input Form

 BellB[n + 1] == Sum[BellB[k] Binomial[n, k], {k, 0, n}] /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BellB", "[", RowBox[List["n", "+", "1"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["BellB", "[", "k", "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BellB", "[", RowBox[List["n_", "+", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List[RowBox[List["BellB", "[", "k", "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2007-05-02