A permutation *f* :{1,2,..., *n*} → {1,2,..., *n*} is said
to be *dispersive* if {|*f*(1) − 1|,
|*f*(2) − 2|,...,
|*f*(*n*) − *n*|} = {0,1,..., *n* − 1}. For example,
the permutation on the left is dispersive, while the one on the right is not. Let
*A _{n}* denote the number of dispersive permutations on
{0,1,...,

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