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 Factorial

 http://functions.wolfram.com/06.01.23.0006.01

 Input Form

 Sum[k!^2/((k + 4)! (k + 8)!), {k, 0, Infinity}] == -(435179/66679200) + Pi^2/1512

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["k", "!"]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["k", "+", "4"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "+", "8"]], ")"]], "!"]]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["435179", "66679200"]]], "+", FractionBox[SuperscriptBox["\[Pi]", "2"], "1512"]]]]]]]

 MathML Form

 k = 0 ( k ! ) 2 ( k + 4 ) ! ( k + 8 ) ! - 435179 66679200 + π 2 1512 k 0 k 2 k 4 k 8 -1 -1 435179 66679200 2 1512 -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_", "!"]], ")"]], "2"], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["k_", "+", "4"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["k_", "+", "8"]], ")"]], "!"]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["435179", "66679200"]]], "+", FractionBox[SuperscriptBox["\[Pi]", "2"], "1512"]]]]]]]

 Contributed by

 Troy Kessler

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

 2007-05-02