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URL: https://oeis.org/A246236

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A246236
Number of rooted trees with n nodes and 7-colored non-root nodes.
2
0, 1, 7, 77, 966, 13342, 195384, 2984142, 46990952, 757504496, 12438875162, 207336046337, 3498937522808, 59663269192765, 1026407662358953, 17792842558962122, 310496318146483175, 5450092704153777190, 96160815834871877516, 1704498464976443234588
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 = 19.21926132906386575759734620749272793..., c = 0.0575798566487866265911656113629518511... . - Vaclav Kotesovec, Aug 26 2014
G.f. A(x) satisfies: A(x) = x*exp(7*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)*7, 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]*7, {j, 1, n-1}]/(n-1)];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 23 2019, from Maple *)
CROSSREFS
Column k=7 of A242249.
Sequence in context: A002281 A097983 A261799 * A349364 A267709 A234466
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 19 2014
STATUS
approved