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A338665 a(n) is the number of preference profiles for n men and n women where every man prefers woman number 1 to woman number 2. 2
4, 5832, 6879707136, 19349176320000000000, 303256405652583481344000000000000, 53311087345695615264200592956011315200000000000000, 190584865366582887488321066784947980317795794157526056960000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
This is also the number of preference profiles for n men and n women where every woman prefers man number 1 to man number 2.
When implementing the men-proposing Gale-Shapley algorithm on such a preference profile, woman number 1 gets her first engagement in an earlier round than woman number 2.
LINKS
FORMULA
a(n) = n!^(2n) / 2^n.
EXAMPLE
When n = 2, we have exactly 1 way to arrange each man's profiles such that woman number 1 is ranked before woman number 2. Each woman's profile can be set in 2! = 2 ways, so the total number of preference profiles such that every man prefers woman number 1 to woman number 2 is 1^2 * 2^2 = 4.
MATHEMATICA
Table[n!^(2 n)/2^n, {n, 2, 10}]
CROSSREFS
Sequence in context: A046360 A367942 A079232 * A137045 A368807 A077258
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, Apr 22 2021
STATUS
approved

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Last modified May 18 09:54 EDT 2024. Contains 372620 sequences. (Running on oeis4.)