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%I #12 Jun 07 2022 15:52:12
%S 0,1,64,104976,8153726976,46656000000000000,
%T 28079296819683655680000000,2400095991902688012207233433600000000,
%U 37800243186554601452585666030525214621696000000000
%N a(n) = (n-1)^n*(n-1)!^n.
%C 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.
%C 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.
%F a(n) = (n-1)^n*(n-1)!^n.
%F a(n) = A065440(n)*A091868(n-1).
%t Table[(n-1)^n*(n-1)!^n,{n,1,9}]
%Y Cf. A065440, A091868, A343694, A343475, A344663, A123234.
%K nonn
%O 1,3
%A _Dan Eilers_, Feb 19 2022
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