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:

(defun fact (n)
  (reduce #'* (loop for i from 1 to n collect i)))

(defun left-fac (n)
  (reduce #'+ (loop for i below n collect (fact i))))

(format t "0 -> 10~&")
(format t "~a~&" (loop for i upto 10 collect (left-fac i)))
(format t "20 -> 110 by 10~&")
(format t "~{~a~&~}" (loop for i from 20 upto 110 by 10 collect (left-fac i)))
(format t "1000 -> 10000 by 1000~&")
(format t "~{~a digits~&~}" (loop for i from 1000 upto 10000 by 1000 collect (length (format nil "~a" (left-fac i)))))