A095349 - OEIS

%I #12 Jul 06 2020 17:06:16

%S 0,1,2,6,12,30,66,161,376,954,2350,6061,15612,41067,108374,289800,

%T 778064,2105739,5723190,15638235,42890100,118098876,326217628,

%U 903897631,2511285360,6994836250,19527701960,54632961864,153147864380,430095282258,1209924870900

%N Total number of edges in all trees on n nodes.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphEdge.html">Graph Edge</a>

%F a(n) = (n-1)*A000055(n). - _Vladeta Jovovic_, Jun 05 2004

%F 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 nn = 25; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol = SolveAlways[0 == Series[

%t f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}], x];

%t r[x_] := Sum[a[n] x^n, {n, 0, nn}] /. sol; Drop[Level[CoefficientList[

%t    Series[x^2 D[1/x (r[x] - 1/2 (r[x]^2 - r[x^2])), x], {x, 0, nn}],

%t x], {2}], 1] (* _Geoffrey Critzer_, Jul 06 2020 *)

%Y Cf. A055543.

%K nonn

%O 1,3

%A _Eric W. Weisstein_, Jun 03 2004