OFFSET
2,1
COMMENTS
This is also the number of preference profiles for n men and n women where every woman prefers man number 1 to man number 2.
When implementing the men-proposing Gale-Shapley algorithm on such a preference profile, woman number 1 gets her first engagement in an earlier round than woman number 2.
LINKS
Wikipedia, Gale-Shapley algorithm.
FORMULA
a(n) = n!^(2n) / 2^n.
EXAMPLE
When n = 2, we have exactly 1 way to arrange each man's profiles such that woman number 1 is ranked before woman number 2. Each woman's profile can be set in 2! = 2 ways, so the total number of preference profiles such that every man prefers woman number 1 to woman number 2 is 1^2 * 2^2 = 4.
MATHEMATICA
Table[n!^(2 n)/2^n, {n, 2, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, Apr 22 2021
STATUS
approved