Definition:Subfactorial

Definition
Let $n \in \Z_{\ge0}$ be a (strictly) positive integer.

The subfactorial of $n$ is defined and denoted as:

It arises as the number of derangements of $n$ distinct objects.

Also denoted as
The subfactorial can also be denoted as $D_n$, where the $D$ derives from derangements.

Also see

 * Closed Form for Number of Derangements on Finite Set
 * Definition:Derangement
 * Hat-Check Problem