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%I #13 Dec 27 2023 16:52:43
%S 0,2,48,2652,251328,34213080,6362490816
%N a(n) is the number of ways to make a Secret Santa assignment among n couples such that no one gets their partner's name and if A gets B's name, B does not get A's name.
%C Equivalent to the number of derangements of [2n] such that (i) there are no 2-cycles, and (ii) neither k nor k+n maps to the other (k <= n).
%C A367538(n) <= a(n) <= A038205(2n) <= A000166(2n), and all the inequalities are strict except for n = 1.
%C Inspired by a question from a coworker about enumerating all possible Secret Santa assignments for an actual Secret Santa exchange for Xmas 2023, subject to these constraints.
%Y Cf. A000166, A038205, A367538.
%K nonn,more
%O 1,2
%A _Jeremy F. Alm_, Nov 21 2023
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