A derangement is a permutation that leaves no element in its original position. For example, (1234) shifts every element over (cyclically), so it is a derangement, but (124) leaves 3 fixed in place, so it is not a derangement. The number of derangements on a set of

elements is called the subfactorial of

(with notation

), given by the formula

, which is highly reminiscent of

. The sequence of subfactorials is

, for

.