Fixed-point-free Permutations

A permutation f is said to be fixed-point-free,
provided there is no x with f(x) = x.

The number of fixed-point-free permutations of an n-element set
is denoted by !n (called "subfactorial" of n),

Example: For n = 3, there are 6 permutations,
the two yellow ones are fixed-point-free:

1

2

3

1

2

3

3 1 2

1

3

2

2 3 1

1

2

3

(the fixed points are marked in red)