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A351781
a(n) = (n-1)^n*(n-1)!^n.
0
0, 1, 64, 104976, 8153726976, 46656000000000000, 28079296819683655680000000, 2400095991902688012207233433600000000, 37800243186554601452585666030525214621696000000000
OFFSET
1,3
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.
FORMULA
a(n) = (n-1)^n*(n-1)!^n.
a(n) = A065440(n)*A091868(n-1).
MATHEMATICA
Table[(n-1)^n*(n-1)!^n, {n, 1, 9}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Dan Eilers, Feb 19 2022
STATUS
approved