Problem Statement

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:

(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:

Display the left factorials for:

Display the length (in decimal digits) of the left factorials for:

Let's start with the solution:

lfactorial: function [n][
    if zero? n -> return 0
    fold 0..dec n [x y] -> x + factorial y
]

print "First eleven:"
0..10 | map => lfactorial
      | print

print "\n20th through 110th by tens:"
r: range.step: 10 20 110
r | map => lfactorial
  | loop => print

print "\nDigits in 1,000th through 10,000th by thousands:"
r: range.step: 1000 1000 10000
r | map'x -> size ~"|lfactorial x|"
  | print