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 A342573 The number of ordered n-tuples consisting of n permutations (not necessarily distinct) such that the first element of each of them is the same. 6
 1, 2, 24, 5184, 39813120, 17915904000000, 702142910300160000000, 3330690501757390081228800000000, 2534703826002712645182542460223488000000000, 395940866122425193243875570782668457763038822400000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is related to the stable marriage problem, as this counts the preference profiles for n men trying to marry n women when all of them prefer the same woman. This sequence also counts the sets of n permutations of size n such that the i-th element of each of them is the same. a(n) is a subsequence of A001013: products of factorial numbers. LINKS Table of n, a(n) for n=1..10. Matvey Borodin, Eric Chen, Aidan Duncan, Tanya Khovanova, Boyan Litchev, Jiahe Liu, Veronika Moroz, Matthew Qian, Rohith Raghavan, Garima Rastogi, and Michael Voigt, Sequences of the Stable Matching Problem, arXiv:2201.00645 [math.HO], 2021. FORMULA a(n) = n*(n-1)!^n = n*A091868(n-1). EXAMPLE When n=3, we have 3 ways to fix the first element, and the remaining elements in each permutation can be in any order, yielding (3 - 1)! possible ways of ordering the rest of each permutation, so there are 3 * (2!)^3 = 24 sets of permutations. MATHEMATICA Table[n (n - 1)!^n, {n, 10}] CROSSREFS Cf. A001013, A091868. Sequence in context: A159907 A242484 A088912 * A203465 A055462 A088600 Adjacent sequences: A342570 A342571 A342572 * A342574 A342575 A342576 KEYWORD nonn AUTHOR Tanya Khovanova and MIT PRIMES STEP Senior group, Mar 27 2021 STATUS approved

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Last modified May 18 08:32 EDT 2024. Contains 372618 sequences. (Running on oeis4.)