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 Factorial

 http://functions.wolfram.com/06.01.23.0009.01

 Input Form

 Sum[k!^3/(k + 4)!^3, {k, 0, Infinity}] == (-6217 + 630 Pi^2)/11664

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["k", "!"]], ")"]], "3"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["k", "+", "4"]], ")"]], "!"]], ")"]], "3"]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["-", "6217"]], "+", RowBox[List["630", " ", SuperscriptBox["\[Pi]", "2"]]]]], "11664"]]]]]

 MathML Form

 k = 0 ( k ! ) 3 ( ( k + 4 ) ! ) 3 - 6217 + 630 π 2 11664 k 0 k 3 k 4 3 -1 -6217 630 2 11664 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["k_", "!"]], ")"]], "3"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["k_", "+", "4"]], ")"]], "!"]], ")"]], "3"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["-", "6217"]], "+", RowBox[List["630", " ", SuperscriptBox["\[Pi]", "2"]]]]], "11664"]]]]]

 Contributed by

 Troy Kessler

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

 2007-05-02