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.

0, 0, 32, 1200, 126720, 17862400, 3403153920

Offset: 1

Author

Jeremy F. Alm, Nov 21 2023

Keywords

• nonn
• more

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

Cf. A000166, A038205, A367537.