VOOZH about

URL: https://oeis.org/A246235

⇱ A246235 - OEIS

login
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
OFFSET
0,3
LINKS
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: A390332 A386938 A371521 * A213105 A138414 A349363
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 19 2014
STATUS
approved