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 A343693 #10 May 27 2021 01:55:11
%S A343693 1,729,429981696,604661760000000000,4738381338321616896000000000000,
%T A343693 416492869888246994251567132468838400000000000000,
%U A343693 744472130338214404251254167128703048116389820927836160000000000000000,45414513879851870274245681660582356320629081347021328317938070440504213897216000000000000000000
%N A343693 a(n) is the number of preference profiles in the stable marriage problem with n men and n women, where every man prefers woman number 1 to woman number 2 and every woman prefers man number 1 to man number 2.
%C A343693 When implementing the men-proposing Gale-Shapley algorithm on such a preference profile, woman number 1's first engagement comes in an earlier round than the first engagement of woman number 2. Similarly, when implementing the women-proposing Gale-Shapley algorithm on such a preference profile, man number 1's first engagement comes in an earlier round than the first engagement for man number 2.
%H A343693 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm">Gale-Shapley algorithm</a>.
%F A343693 a(n) = n!^(2*n) / 4^n.
%F A343693 a(n) = A338665(n)/2^n = A343692(n)^2.
%e A343693 When n = 2, each man and each woman have fixed preferences, so every person has exactly 1 way to set their personal preferences, yielding 1 total preference profile.
%t A343693 Table[n!^(2 n)/4^n, {n, 2, 10}]
%Y A343693 Cf. A185141, A338665, A343474, A343692.
%K A343693 nonn
%O A343693 2,2
%A A343693 _Tanya Khovanova_ and MIT PRIMES STEP Senior group, May 24 2021