

A343692


a(n) is the number of men's preference profiles in the stable marriage problem with n men and n women, where every man prefers woman number 1 to woman number 2.


1



1, 27, 20736, 777600000, 2176782336000000, 645362587921121280000000, 27285016590396539545426329600000000, 213106813311662727500673631554480635904000000000, 386661002072680852777222237092449665784217600000000000000000000
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OFFSET

2,2


COMMENTS

When implementing the menproposing GaleShapley algorithm on such a preference profile, woman number 1's first engagement comes in an earlier round than the engagement of woman number 2.
This is the same as the number of women's preference profiles in the stable marriage problem with n men and n women, where every woman prefers man number 1 to man number 2.


LINKS



FORMULA

a(n) = n!^(n) / 2^n.


EXAMPLE

When n = 2, there is exactly 1 way for each man's profile to be completed such that woman number 1 is before woman number 2. Since we are only looking at men's profiles, this means there are 1^n = 1^2 = 1 preference profiles such that every man prefers woman number 1 to woman number 2.


MATHEMATICA

Table[n!^n/2^n, {n, 2, 10}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



