A344693 a(n) is the number of joint preference profiles in a stable marriage problem with n men and n women.

1, 4, 72, 13824, 19353600, 585252864000, 309856276316160000, 4385849628750224818176000, 2004821822925413274697731145728000, 36224269774123479086515914989912457216000000, 31014029806101314488308034499720939299674343342080000000

Offset: 1

Author

Tanya Khovanova and MIT PRIMES STEP Senior group, Jun 11 2021

Keywords

• nonn

Comments

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).

In such a profile the ranking matrix of women's preferences forms a Latin square. The same is true for men's preferences.

Examples

			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.
		

Crossrefs

Cf. A185141, A002860.

Formula

a(n) = n!*A002860(n)