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
.
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