derangement numbers

derangement numbers

[di′rānj·mənt ‚nəm·bərz]
(mathematics)
The numbers Dn, n = 1, 2, 3, …, giving the number of permutations of a set of n elements that carry no element of the set into itself.
References in periodicals archive ?
n] stand for the number of (n, k)-permutations; these are the rencontre numbers, which are related to the derangement numbers by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Interestingly, this formula, which is a combination of factorials, can also be written as the same combination of an infinite family of other numbers, including the derangement numbers.