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 Fibonacci

 http://functions.wolfram.com/04.11.06.0006.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29