OFFSET
1,2
COMMENTS
For these profiles both men-proposing and women-proposing Gale-Shapley algorithms end in one round.
This is a subsequence of A001013.
LINKS
Wikipedia, Gale-Shapley algorithm.
FORMULA
a(n) = n!^2 * (n-1)!^(2n).
a(n) = A343694(n)^2.
EXAMPLE
When n = 3, there are 3! ways for men to pick their first choices and 2!^3 ways to complete their lists of preferences. The same calculation works for women's preferences. As the preferences of different genders are independent, we have a total of 3!^2 * 2!^6 = 2304 such preference profiles for n = 3.
MATHEMATICA
Table[n!^2 (n - 1)!^(2 n), {n, 10}].
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, May 25 2021
STATUS
approved