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 A095349 #13 Feb 16 2025 08:32:53
%S A095349 0,1,2,6,12,30,66,161,376,954,2350,6061,15612,41067,108374,289800,
%T A095349 778064,2105739,5723190,15638235,42890100,118098876,326217628,
%U A095349 903897631,2511285360,6994836250,19527701960,54632961864,153147864380,430095282258,1209924870900
%N A095349 Total number of edges in all trees on n nodes.
%H A095349 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphEdge.html">Graph Edge</a>
%F A095349 a(n) = (n-1)*A000055(n). - _Vladeta Jovovic_, Jun 05 2004
%F A095349 O.g.f.: x^2 d/dx(A(x)-1)/x where A(x) is the o.g.f. for A000055. - _Geoffrey Critzer_, Jul 06 2020
%t A095349 nn = 25; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol = SolveAlways[0 == Series[
%t A095349 f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}], x];
%t A095349 r[x_] := Sum[a[n] x^n, {n, 0, nn}] /. sol; Drop[Level[CoefficientList[
%t A095349 Series[x^2 D[1/x (r[x] - 1/2 (r[x]^2 - r[x^2])), x], {x, 0, nn}],
%t A095349 x], {2}], 1] (* _Geoffrey Critzer_, Jul 06 2020 *)
%Y A095349 Cf. A055543.
%K A095349 nonn
%O A095349 1,3
%A A095349 _Eric W. Weisstein_, Jun 03 2004