A343694 a(n) is the number of men's preference profiles in the stable marriage problem with n men and n women, such that all men prefer different women as their first choices.

1, 2, 48, 31104, 955514880, 2149908480000000, 505542895416115200000000, 16786680128857246009393152000000000, 102199258264429373853760111996211036160000000000, 143679021498505654124337567125614729953051527872512000000000000

Offset: 1

Author

Tanya Khovanova and MIT PRIMES STEP Senior group, May 25 2021

Keywords

• nonn

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.

Examples

			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.
		

Links

• Wikipedia, Gale-Shapley algorithm.

Crossrefs

Cf. A001013, A185141, A343474, A343695, A342573, A340890.

Programs

Mathematica

Table[n! (n - 1)!^n, {n, 10}]

Formula

a(n) = n! * (n-1)!^n.