A350558 a(n) = (n-1)!^(2n).

1, 1, 64, 1679616, 63403380965376, 8916100448256000000000000, 10061319724179153710638694400000000000000, 173335925289013982808975076100021379095592960000000000000000, 79317573895713454077105543742169655162315106629579798748776628224000000000000000000

Offset

1,3

Comments

a(n) is the number of ways to arrange the remaining preferences in the stable marriage problem of order n after the first choice of each participant has been determined. The first choices are often treated separately in order to avoid mutual first choices, or to avoid multiple participants with the same first choice.

Links

Table of n, a(n) for n=1..9.

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-1)!^(2n).

a(n) = A343700(n)/A284458(n).

a(n) = A343698(n)/A000142(n).

a(n) = A343699(n)/((n-1)!*n^2*(n^2-1)).

a(n) = A343699(n)/(A000142(n)*n*(n^2-1)).

Mathematica

Table[(n-1)!^(2n), {n, 1, 9}]

Crossrefs

Cf. A000142, A284458, A343698, A343699, A343700.

Sequence in context: A203255 A232722 A017094 * A160864 A017190 A329236

Adjacent sequences: A350555 A350556 A350557 * A350559 A350560 A350561

Keyword

nonn

Author

Dan Eilers, Feb 15 2022

Status

approved