A375105 - OEIS

%I #9 Jul 30 2024 14:38:54

%S 1,12,720,107520,30240000,13795246080,9302892318720,8706006083174400,

%T 10801536141415219200,17163329863680000000000,

%U 33994996578425904640819200,82126085558902590463908249600,237708952408715572102802964480000,812136157489332816782291600670720000

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

%C 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.

%H Danyi Li, Xing Feng, and Weigen Yan, <a href="https://doi.org/10.1016/j.dam.2024.07.026">Enumeration of spanning trees with a perfect matching of hexagonal lattices on the cylinder and Möbius strip</a>, Discrete Applied Mathematics, Volume 358, 2024, Pages 320-325.

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

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

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

%K nonn

%O 1,2

%A _Stefano Spezia_, Jul 30 2024