(derangements 4)
    → ((3 0 1 2) (2 0 3 1) (2 3 0 1) (3 2 0 1) (3 2 1 0) (2 3 1 0) (1 2 3 0) (1 3 0 2) (1 0 3 2))

;; generated versus computed

(for ((i 10)) (writeln i '| (count-derangements i) (!n i)))

0     |     1     1
1     |     0     0
2     |     1     1
3     |     2     2
4     |     9     9
5     |     44     44
6     |     265     265
7     |     1854     1854
8     |     14833     14833
9     |     133496     133496

(!n 20)
    → 895014631192902121