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 A356259 #8 Aug 04 2022 15:54:52
%S A356259 0,2,6,60,500,7290,100842,1978368,38263752,949218750,23579476910,
%T A356259 709026379776,21505924728444,760772509715764,27246730957031250,
%U A356259 1109165339867873280,45798768824157052688,2109518949433090534902
%N A356259 Number of labeled rooted trees on [n] that have a primary branch.
%C A356259 This sequence is the labeled version of A027415 where the definition can be found.
%H A356259 N. J. A. Sloane, <a href="/A000081/a000081.html">Illustration of initial terms</a>
%F A356259 a(n) = Sum_{i=1..floor(n/2)} binomial(n,n-i)*r(n-i)*r(i) where r(i) = A000169(i).
%F A356259 a(n) = A000169(n) - A356073(n).
%e A356259 a(5) = 500. In the illustrations by Sloane found in the link above, for n = 5, there are A027415(5) = 6 rooted trees with a primary branch: the first six trees shown.
%t A356259 Table[Sum[Binomial[n, n - i] (n - i)^(n - i - 1)*i^(i - 1), {i, 1,Floor[n/2]}], {n, 1, 20}]
%Y A356259 Cf. A027415, A356074, A000169.
%K A356259 nonn
%O A356259 1,2
%A A356259 _Geoffrey Critzer_, Jul 31 2022