A055543 Total number of nodes in all trees with n nodes.

1, 2, 3, 8, 15, 36, 77, 184, 423, 1060, 2585, 6612, 16913, 44226, 116115, 309120, 826693, 2229606, 6041145, 16461300, 45034605, 123722632, 341045702, 943197528, 2615922250, 7274629700, 20278767420, 56656404896, 158617430965, 444926154060, 1250255699930

Offset

1,2

Links

Table of n, a(n) for n=1..31.

Eric Weisstein's World of Mathematics, Graph Vertex.

Index entries for sequences related to trees

Formula

a(n) = n*A000055(n).

O.g.f.: x d/dx A(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; CoefficientList[Series[x D[r[x] - 1/2 (r[x]^2 - r[x^2]), x], {x, 0, nn}], x] (* Geoffrey Critzer, Jul 06 2020 *)

Crossrefs

Cf. A000055, A000169, A055542, A055544.

Sequence in context: A242510 A080206 A132862 * A308433 A049957 A151255

Adjacent sequences: A055540 A055541 A055542 * A055544 A055545 A055546

Keyword

nonn,easy

Author

Eric W. Weisstein

Extensions

More terms, formula from Christian G. Bower, Jun 12 2000

Status

approved