A351781 a(n) = (n-1)^n*(n-1)!^n.

0, 1, 64, 104976, 8153726976, 46656000000000000, 28079296819683655680000000, 2400095991902688012207233433600000000, 37800243186554601452585666030525214621696000000000

Offset: 1

Author

Dan Eilers, Feb 19 2022

Keywords

• nonn

Comments

a(n) is the number of women's ranking tables in the stable marriage problem that can be paired with a men's ranking table having no two men with the same first choice, without forming any mutual first choices. It has two terms: (n-1)^n from A065440(n), and (n-1)!^n from A091868(n-1). Such men's ranking tables having no two men with the same first choice arise in A343694, A343475, and A344663.

a(n)*A123234 is a useful alternative to A343696 which combines a Latin men's ranking table with an arbitrary women's table, since it gives fewer instances to consider.

Crossrefs

Cf. A065440, A091868, A343694, A343475, A344663, A123234.

Programs

Mathematica

Table[(n-1)^n*(n-1)!^n,{n,1,9}]

Formula

a(n) = (n-1)^n*(n-1)!^n.

a(n) = A065440(n)*A091868(n-1).