A375105 a(n) = (2*n)^(n-2)*(2*n)!/n!.

1, 12, 720, 107520, 30240000, 13795246080, 9302892318720, 8706006083174400, 10801536141415219200, 17163329863680000000000, 33994996578425904640819200, 82126085558902590463908249600, 237708952408715572102802964480000, 812136157489332816782291600670720000

Offset: 1

Author

Stefano Spezia, Jul 30 2024

Keywords

• nonn

Comments

a(n) is the number of spanning trees with a perfect matching in a complete graph with 2*n nodes. See Li et al. in Links.

Links

• Danyi Li, Xing Feng, and Weigen Yan, Enumeration of spanning trees with a perfect matching of hexagonal lattices on the cylinder and Möbius strip, Discrete Applied Mathematics, Volume 358, 2024, Pages 320-325.

Crossrefs

Cf. A000142, A000984, A010050, A020765, A135008.

Programs

Mathematica

a[n_]:=(2n)^(n-2)(2n)!/n!; Array[a,14]

Formula

a(n) ~ (1/(2*sqrt(2)))*(8/e)^n*n^(2*(n-1)).