This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356186 #46 Jul 31 2022 19:52:48
%S A356186 0,1,12,810,143360,49218750,27935373312,23751648836916,
%T A356186 28301429298954240,45046920790988254710,92378000000000000000000,
%U A356186 237289687212632836205339916,746430126201849206626773368832,2822726846177838977566127355808300
%N A356186 Number of labeled trees on [2n] with a bicentroid.
%C A356186 This sequence is the labeled version of A102911 where the pertinent definitions can be found.
%H A356186 N. J. A. Sloane, <a href="/A000055/a000055.gif">Illustration of initial terms</a>
%F A356186 a(n) = binomial(2n,n)*n^(2n-2)/2 = A000984(n)*A000169(n)^2/2.
%e A356186 a(3) = 810. In the illustrations by Sloane found in the link above, for n = 6, there are A102911(3) = 3 trees with a bicentroid: the first, second and last trees shown. They have 360, 360, and 90 labelings respectively. 360 + 360 + 90 = 810.
%t A356186 Prepend[Table[Binomial[2 n, n] n^(n - 1) n^(n - 1)/2, {n, 1, 12}], 0]
%Y A356186 Cf. A102911, A000984, A000169.
%K A356186 nonn
%O A356186 0,3
%A A356186 _Geoffrey Critzer_, Jul 31 2022