Number of derangements

Remarks

The first values, for $n = 0, 1, \dots, 6$, are $1, 0, 1, 2, 9, 44, 265$. The value $D_n$ is the number of derangements of an $n$-element set. The node the derangement numbers count derangements states this. Another notation is $!n$, the subfactorial of $n$.