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A343694 a(n) is the number of men's preference profiles in the stable marriage problem with n men and n women, such that all men prefer different women as their first choices. 4
1, 2, 48, 31104, 955514880, 2149908480000000, 505542895416115200000000, 16786680128857246009393152000000000, 102199258264429373853760111996211036160000000000, 143679021498505654124337567125614729953051527872512000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For such a preference profile, the men-proposing Gale-Shapley algorithm ends in one round since each woman receives exactly one proposal in the first round.
This sequence also counts the preference profiles for n men who rank n women such that all men prefer different women as their i-th choice, for an i between 1 and n, inclusive.
LINKS
FORMULA
a(n) = n! * (n-1)!^n.
EXAMPLE
For n=2, there are two ways to pick men's first preferences, and then one way to complete the preference profile, making a total of 2 preference profiles.
MATHEMATICA
Table[n! (n - 1)!^n, {n, 10}]
CROSSREFS
Sequence in context: A081960 A123742 A203311 * A295177 A098694 A137592
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, May 25 2021
STATUS
approved

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Last modified May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)