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 A340890 a(n) is the number of preference profiles for n men and n women, where all men prefer the same woman. 5
 1, 8, 5184, 1719926784, 990677827584000000, 2495937495082991616000000000000, 58001506007267709490243656115814400000000000000, 23264754073069200132851692722771970253637181903994880000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. a(n) = n!^n A342573(n), where A342573 ignores women's preferences. a(n) is a subsequence of A001013. LINKS 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. FORMULA a(n) = n(n-1)!^n * n!^n. EXAMPLE When n=2, the total number of profiles is 16, and in half of them, the same woman is ranked 1st by both men. MATHEMATICA Table[n (n - 1)!^n n!^n, {n, 10}] CROSSREFS Cf. A001013, A185141, A342573. Sequence in context: A055319 A029736 A206460 * A093937 A318897 A178329 Adjacent sequences: A340887 A340888 A340889 * A340891 A340892 A340893 KEYWORD nonn AUTHOR Tanya Khovanova and MIT PRIMES STEP Senior group, Mar 31 2021 STATUS approved

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Last modified December 6 04:57 EST 2022. Contains 358594 sequences. (Running on oeis4.)