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 A344693 #7 Jan 27 2022 23:16:33 %S A344693 1,4,72,13824,19353600,585252864000,309856276316160000, %T A344693 4385849628750224818176000,2004821822925413274697731145728000, %U A344693 36224269774123479086515914989912457216000000,31014029806101314488308034499720939299674343342080000000 %N A344693 a(n) is the number of joint preference profiles in a stable marriage problem with n men and n women. %C A344693 A joint profile is defined as a preference profile with a fixed function f(k), such that for every man ranked k by a woman, he has to rank her back as f(k). %C A344693 In such a profile the ranking matrix of women's preferences forms a Latin square. The same is true for men's preferences. %F A344693 a(n) = n!*A002860(n) %e A344693 For n=2, there are two types of joint profiles. In the first type, the mutual rankings are (1,1) and (2,2). In the second type, the mutual rankings are (1,2) and (2,1). For each type, the profile is uniquely defined after choosing the woman to be the first choice for the first man (there are two ways to do it). Therefore, a(2) = 4. %Y A344693 Cf. A185141, A002860. %K A344693 nonn %O A344693 1,2 %A A344693 _Tanya Khovanova_ and MIT PRIMES STEP Senior group, Jun 11 2021