'''Left factorials''',   !n,   may refer to either   ''subfactorials''   or to   ''factorial sums'';
the same notation can be confusingly seen used for the two different definitions. Sometimes,   ''subfactorials''   (also known as ''derangements'')   may use any of the notations: :::::::*   !''n''` :::::::*   !''n'' :::::::*   ''n''¡ (It may not be visually obvious, but the last example uses an upside-down exclamation mark.)
This Rosetta Code task will be using this formula for '''left factorial''': :::   $!n\; =\; \backslash sum\_\{k=0\}^\{n-1\}\; k!$ where :::   $!0\; =\; 0$ ;Task Display the left factorials for: * zero through ten (inclusive) * 20 through 110 (inclusive) by tens
Display the length (in decimal digits) of the left factorials for: * 1,000,   2,000   through   10,000   (inclusive), by thousands. ;Also see *   The OEIS entry: [http://oeis.org/A003422 A003422 left factorials] *   The MathWorld entry: [http://mathworld.wolfram.com/LeftFactorial.html left factorial] *   The MathWorld entry: [http://mathworld.wolfram.com/FactorialSums.html factorial sums] *   The MathWorld entry: [http://mathworld.wolfram.com/Subfactorial.html subfactorial] ;Related task: *   [http://rosettacode.org/wiki/Permutations/Derangements permutations/derangements (subfactorials)]