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 A338665 #15 May 27 2021 06:56:01
%S A338665 4,5832,6879707136,19349176320000000000,
%T A338665 303256405652583481344000000000000,
%U A338665 53311087345695615264200592956011315200000000000000,190584865366582887488321066784947980317795794157526056960000000000000000
%N A338665 a(n) is the number of preference profiles for n men and n women where every man prefers woman number 1 to woman number 2.
%C A338665 This is also the number of preference profiles for n men and n women where every woman prefers man number 1 to man number 2.
%C A338665 When implementing the men-proposing Gale-Shapley algorithm on such a preference profile, woman number 1 gets her first engagement in an earlier round than woman number 2.
%H A338665 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm">Gale-Shapley algorithm</a>.
%F A338665 a(n) = n!^(2n) / 2^n.
%e A338665 When n = 2, we have exactly 1 way to arrange each man's profiles such that woman number 1 is ranked before woman number 2. Each woman's profile can be set in 2! = 2 ways, so the total number of preference profiles such that every man prefers woman number 1 to woman number 2 is 1^2 * 2^2 = 4.
%t A338665 Table[n!^(2 n)/2^n, {n, 2, 10}]
%Y A338665 Cf. A001013, A185141, A342573, A340890, A343474, A343475.
%K A338665 nonn
%O A338665 2,1
%A A338665 _Tanya Khovanova_ and MIT PRIMES STEP Senior group, Apr 22 2021