A095349 Total number of edges in all trees on n nodes.

0, 1, 2, 6, 12, 30, 66, 161, 376, 954, 2350, 6061, 15612, 41067, 108374, 289800, 778064, 2105739, 5723190, 15638235, 42890100, 118098876, 326217628, 903897631, 2511285360, 6994836250, 19527701960, 54632961864, 153147864380, 430095282258, 1209924870900

Offset: 1

Author

Eric W. Weisstein, Jun 03 2004

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Graph Edge

Crossrefs

Cf. A055543.

Programs

Mathematica

nn = 25; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol = SolveAlways[0 == Series[
f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}], x];
r[x_] := Sum[a[n] x^n, {n, 0, nn}] /. sol; Drop[Level[CoefficientList[
   Series[x^2 D[1/x (r[x] - 1/2 (r[x]^2 - r[x^2])), x], {x, 0, nn}],
x], {2}], 1] (* Geoffrey Critzer, Jul 06 2020 *)

Formula

a(n) = (n-1)*A000055(n). - Vladeta Jovovic, Jun 05 2004

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