OFFSET
1,2
COMMENTS
For such a preference profile, the men-proposing Gale-Shapley algorithm ends in one round since each woman receives exactly one proposal in the first round.
This sequence also counts the preference profiles for n men who rank n women such that all men prefer different women as their i-th choice, for an i between 1 and n, inclusive.
LINKS
Wikipedia, Gale-Shapley algorithm.
FORMULA
a(n) = n! * (n-1)!^n.
EXAMPLE
For n=2, there are two ways to pick men's first preferences, and then one way to complete the preference profile, making a total of 2 preference profiles.
MATHEMATICA
Table[n! (n - 1)!^n, {n, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, May 25 2021
STATUS
approved