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A246236 Number of rooted trees with n nodes and 7-colored non-root nodes. 2

%I

%S 0,1,7,77,966,13342,195384,2984142,46990952,757504496,12438875162,

%T 207336046337,3498937522808,59663269192765,1026407662358953,

%U 17792842558962122,310496318146483175,5450092704153777190,96160815834871877516,1704498464976443234588

%N Number of rooted trees with n nodes and 7-colored non-root nodes.

%H Alois P. Heinz, <a href="/A246236/b246236.txt">Table of n, a(n) for n = 0..500</a>

%H Loïc Foissy, <a href="https://arxiv.org/abs/1811.07572">Algebraic structures on typed decorated rooted trees</a>, arXiv:1811.07572 [math.RA], 2018.

%F a(n) ~ c * d^n / n^(3/2), where d = 19.21926132906386575759734620749272793..., c = 0.0575798566487866265911656113629518511... . - _Vaclav Kotesovec_, Aug 26 2014

%F G.f. A(x) satisfies: A(x) = x*exp(7*Sum_{k>=1} A(x^k)/k). - _Ilya Gutkovskiy_, Mar 20 2018

%p with(numtheory):

%p a:= proc(n) option remember; `if`(n<2, n, (add(add(d*

%p a(d), d=divisors(j))*a(n-j)*7, j=1..n-1))/(n-1))

%p end:

%p seq(a(n), n=0..25);

%t 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)];

%t Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Feb 23 2019, from Maple *)

%Y Column k=7 of A242249.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Aug 19 2014

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Last modified July 2 08:50 EDT 2020. Contains 335398 sequences. (Running on oeis4.)