

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
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OFFSET

1,2


COMMENTS

This is the same number of preference profiles as when all men rank the same woman at the ith 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.


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(n1)!^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



KEYWORD

nonn


AUTHOR



STATUS

approved



