A246235 Number of rooted trees with n nodes and 6-colored non-root nodes.

0, 1, 6, 57, 614, 7284, 91566, 1200705, 16232820, 224669049, 3167546164, 45332076360, 656839389030, 9616669678368, 142047629163678, 2114254565121153, 31678697416852592, 477435309876933207, 7232846873430148224, 110080098299375941607, 1682316692754904517268

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Loïc Foissy, Algebraic structures on typed decorated rooted trees, arXiv:1811.07572 [math.RA], 2018.

Formula

a(n) ~ c * d^n / n^(3/2), where d = 16.50220884469300156571122110433906696332..., c = 0.06729936839826481812867613714374483... . - Vaclav Kotesovec, Aug 20 2014

G.f. A(x) satisfies: A(x) = x*exp(6*Sum_{k>=1} A(x^k)/k). - Ilya Gutkovskiy, Mar 20 2018

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n<2, n, (add(add(d*
      a(d), d=divisors(j))*a(n-j)*6, j=1..n-1))/(n-1))
    end:
seq(a(n), n=0..25);

Mathematica

a[n_] := a[n] = If[n<2, n, Sum[Sum[d*a[d], {d, Divisors[j]}]*a[n-j]*6, {j, 1, n-1}]/(n-1)];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 23 2019, translated from Maple *)

Crossrefs

Column k=6 of A242249.

Sequence in context: A161434 A332620 A371521 * A213105 A138414 A349363

Adjacent sequences: A246232 A246233 A246234 * A246236 A246237 A246238

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2014

Status

approved