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