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A095349 Total number of edges in all trees on n nodes. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Graph Edge
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
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 *)
CROSSREFS
Cf. A055543.
Sequence in context: A161507 A335711 A032177 * A291518 A291445 A320664
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 03 2004
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)