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A246235 Number of rooted trees with n nodes and 6-colored non-root nodes. 2
0, 1, 6, 57, 614, 7284, 91566, 1200705, 16232820, 224669049, 3167546164, 45332076360, 656839389030, 9616669678368, 142047629163678, 2114254565121153, 31678697416852592, 477435309876933207, 7232846873430148224, 110080098299375941607, 1682316692754904517268 (list; graph; refs; listen; history; text; internal format)
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: A095900 A161434 A332620 * A213105 A138414 A130565

Adjacent sequences:  A246232 A246233 A246234 * A246236 A246237 A246238

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 19 2014

STATUS

approved

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Last modified July 5 20:21 EDT 2020. Contains 335473 sequences. (Running on oeis4.)