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A367538
a(n) is the number of ways to make a Secret Santa assignment among n couples such that (i) no one gets their partner's name, (ii) if A gets B's name, B does not get A's name, and (iii) if A gets B's name, then A's partner does not get B's partner's name.
1
0, 0, 32, 1200, 126720, 17862400, 3403153920
OFFSET
1,3
COMMENTS
Equivalent to the number of derangements of [2n] such that (i) there are no 2-cycles, (ii) neither k nor k+n maps to the other (k <= n), and (iii) we never have that both k maps to m and k+n maps to m+n.
a(n) <= A367537(n) <= A038205(2n) <= A000166(2n), and all the inequalities are strict except for n = 1.
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.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jeremy F. Alm, Nov 21 2023
STATUS
approved