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 Factorial

 http://functions.wolfram.com/06.01.23.0013.01

 Input Form

 Sum[k!^3/(k + 5)!^3, {k, 0, Infinity}] == (5 (1728 Zeta[3] - 2077))/1327104

 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", "+", "5"]], ")"]], "!"]], ")"]], "3"]]]], "\[Equal]", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["1728", " ", RowBox[List["Zeta", "[", "3", "]"]]]], "-", "2077"]], ")"]]]], "1327104"]]]]]

 MathML Form

 k = 0 ( k ! ) 3 ( ( k + 5 ) ! ) 3 5 ( 1728 ζ ( 3 ) TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e\$, Zeta[BoxForm`e\$]]]] - 2077 ) 1327104 k 0 k 3 k 5 3 -1 5 1728 Zeta 3 -2077 1327104 -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_", "+", "5"]], ")"]], "!"]], ")"]], "3"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["1728", " ", RowBox[List["Zeta", "[", "3", "]"]]]], "-", "2077"]], ")"]]]], "1327104"]]]]]

 Contributed by

 Troy Kessler

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

 2007-05-02