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 A055543 #18 Feb 16 2025 08:32:43
%S A055543 1,2,3,8,15,36,77,184,423,1060,2585,6612,16913,44226,116115,309120,
%T A055543 826693,2229606,6041145,16461300,45034605,123722632,341045702,
%U A055543 943197528,2615922250,7274629700,20278767420,56656404896,158617430965,444926154060,1250255699930
%N A055543 Total number of nodes in all trees with n nodes.
%H A055543 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphVertex.html">Graph Vertex.</a>
%H A055543 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A055543 a(n) = n*A000055(n).
%F A055543 O.g.f.: x d/dx A(x) where A(x) is the o.g.f. for A000055. - _Geoffrey Critzer_, Jul 06 2020
%t A055543 nn = 25; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol = SolveAlways[0 == Series[
%t A055543 f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}], x];
%t A055543 r[x_] := Sum[a[n] x^n, {n, 0, nn}] /. sol; CoefficientList[Series[x D[r[x] - 1/2 (r[x]^2 - r[x^2]), x], {x, 0, nn}], x] (* _Geoffrey Critzer_, Jul 06 2020 *)
%Y A055543 Cf. A000055, A000169, A055542, A055544.
%K A055543 nonn,easy
%O A055543 1,2
%A A055543 _Eric W. Weisstein_
%E A055543 More terms, formula from _Christian G. Bower_, Jun 12 2000