A367537 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.

0, 2, 48, 2652, 251328, 34213080, 6362490816

Offset

1,2

Comments

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).

A367538(n) <= a(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.

Links

Table of n, a(n) for n=1..7.

Crossrefs

Cf. A000166, A038205, A367538.

Sequence in context: A210723 A346454 A322750 * A346019 A087085 A067626

Adjacent sequences: A367534 A367535 A367536 * A367538 A367539 A367540

Keyword

nonn,more

Author

Jeremy F. Alm, Nov 21 2023

Status

approved