A344690 a(n) is the number of multisets of size n consisting of permutations of n elements.

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

Offset: 1

Author

Tanya Khovanova and MIT PRIMES STEP Senior group, Jun 04 2021

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A185141.

Programs

Mathematica

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

Formula

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