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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
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
KEYWORD
nonn
AUTHOR
Tanya Khovanova and MIT PRIMES STEP Senior group, Jun 04 2021
STATUS
approved

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