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A340890
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a(n) is the number of preference profiles for n men and n women, where all men prefer the same woman.
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5
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1, 8, 5184, 1719926784, 990677827584000000, 2495937495082991616000000000000, 58001506007267709490243656115814400000000000000, 23264754073069200132851692722771970253637181903994880000000000000000
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OFFSET
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1,2
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COMMENTS
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This is the same number of preference profiles as when all men rank the same woman at the i-th place, where i can be anywhere from 1 to n.
Note that we can swap men and women in the definition of the sequence.
The total number of possible profiles is A185141.
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LINKS
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Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, Sequences of the Stable Matching Problem, arXiv:2201.00645 [math.HO], 2021.
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FORMULA
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a(n) = n(n-1)!^n * n!^n.
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EXAMPLE
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When n=2, the total number of profiles is 16, and in half of them, the same woman is ranked 1st by both men.
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MATHEMATICA
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Table[n (n - 1)!^n n!^n, {n, 10}]
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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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