This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A343694 #9 Jun 09 2021 02:39:04
%S A343694 1,2,48,31104,955514880,2149908480000000,505542895416115200000000,
%T A343694 16786680128857246009393152000000000,
%U A343694 102199258264429373853760111996211036160000000000,143679021498505654124337567125614729953051527872512000000000000
%N 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.
%C A343694 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.
%C A343694 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.
%H A343694 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm">Gale-Shapley algorithm</a>.
%F A343694 a(n) = n! * (n-1)!^n.
%e A343694 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.
%t A343694 Table[n! (n - 1)!^n, {n, 10}]
%Y A343694 Cf. A001013, A185141, A343474, A343695, A342573, A340890.
%K A343694 nonn
%O A343694 1,2
%A A343694 _Tanya Khovanova_ and MIT PRIMES STEP Senior group, May 25 2021