This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344690 #7 Jun 07 2021 09:35:39
%S A344690 1,3,56,17550,225150024,197554684517400,16458566311785642529680,
%T A344690 173358539198065045263504881415600,
%U A344690 300709637734376436340098187751948137677075840,109112041481912234203213339867180762753584908387010487351680
%N A344690 a(n) is the number of multisets of size n consisting of permutations of n elements.
%C A344690 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.
%F A344690 a(n) = binomial(n! + n - 1, n).
%e A344690 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.
%t A344690 %Table[Binomial[Factorial[n] + n - 1, n], {n, 10}]
%Y A344690 Cf. A185141.
%K A344690 nonn
%O A344690 1,2
%A A344690 _Tanya Khovanova_ and MIT PRIMES STEP Senior group, Jun 04 2021