The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..10. 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 Cf. A185141. Sequence in context: A070731 A132489 A350336 * A203483 A051227 A122548 Adjacent sequences: A344687 A344688 A344689 * A344691 A344692 A344693 KEYWORD nonn AUTHOR Tanya Khovanova and MIT PRIMES STEP Senior group, Jun 04 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)