

A344690


a(n) is the number of multisets of size n consisting of permutations of n elements.


1



1, 3, 56, 17550, 225150024, 197554684517400, 16458566311785642529680, 173358539198065045263504881415600, 300709637734376436340098187751948137677075840, 109112041481912234203213339867180762753584908387010487351680
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OFFSET

1,2


COMMENTS

a(n) is the number of different men's preference profiles in the stable marriage problem with n men and n women up to relabeling the men.


LINKS



FORMULA

a(n) = binomial(n! + n  1, n).


EXAMPLE

Consider n = 3. If all three permutations are the same then there are 6 possibilities from which permutation to choose. If two permutations are the same (6 possibilities for each) and the third permutation is different (5 permutations left), then the number of possibilities is 30. If all three permutations are different, then the number of ways to choose them is 6 * 5 * 4/6 = 20. Thus, a(3) = 20 + 30 + 6 = 56.


MATHEMATICA

%Table[Binomial[Factorial[n] + n  1, n], {n, 10}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



