Left factorials,   !n,   may refer to either   subfactorials   or to   factorial sums;

the same notation can be confusingly seen being 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   (factorial sums)   for   left factorial:


   



!
n
=

∑

k
=
0


n
−
1


k
!


{\displaystyle !n=\sum _{k=0}^{n-1}k!}




 where


   



!
0
=
0


{\displaystyle !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   through   10,000   (inclusive), by thousands.


Also see

   The OEIS entry: A003422 left factorials
   The MathWorld entry: left factorial
   The MathWorld entry: factorial sums
   The MathWorld entry: subfactorial


Related task

   permutations/derangements (subfactorials)


leftFact :: [Integer]
leftFact = scanl (+) 0 fact
 
fact :: [Integer]
fact = scanl (*) 1 [1 ..]
 
main :: IO ()
main =
  mapM_
    putStrLn
    [ "0 ~ 10:"
    , show $ (leftFact !!) <$> [0 .. 10]
    , ""
    , "20 ~ 110 by tens:"
    , unlines $ show . (leftFact !!) <$> [20,30 .. 110]
    , ""
    , "length of 1,000 ~ 10,000 by thousands:"
    , show $ length . show . (leftFact !!) <$> [1000,2000 .. 10000]
    , ""
    ]