The Subfactorials

Subfactorials are the dearrangements of a set
That is, the permutations of a set of elements where all elements are out of order
e.g. The dearrangements of (1,2,3) are (3,1,2) and (2,3,1)

d(1) = 0, d(2) = 1

Then d(N) = (N-1)[ d(N-1) + d(N-2) ]
e.g. d(3) = (2)[1 + 0] = 2

The first few are 0, 1, 2, 9, 44, 265, 1854, ...

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