OFFSET
1,2
COMMENTS
In the Stable Marriage Problem, the men's and women's preference lists can be swapped without affecting the number of blocking pairs or stable matchings, because the definitions of blocking pairs and stable matchings are symmetrical with respect to gender. a(n) is the number of instances in a canonical form where the men's preferences are lexicographically less than or equal to the women's preferences.
The A185141(n) instances of order n can be arranged in a square table with rows and columns indexed respectively by all possible men's and women's preferences in lexical order. The main diagonal of the square would be instances with men's preferences equal to women's preferences. The upper triangular region above the diagonal would contain instances with men's preferences less than women's preferences. The number of rows and columns in the table is given by A036740. The number of elements in the upper triangular region of a square, including the diagonal, is given by A000217. So a(n) composes A000217 with A036740 (performing A036740 first).
LINKS
EXAMPLE
MATHEMATICA
Table[((n!)^n) * ((n!)^n + 1) / 2, {n, 1, 8}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Dan Eilers, Jan 29 2023
STATUS
approved