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A246239 Number of rooted trees with n nodes and 10-colored non-root nodes.

%I A246239 #17 Feb 23 2019 10:12:59
%S A246239 0,1,10,155,2770,54465,1136402,24723000,554540590,12732651160,
%T A246239 297795974970,7069820334023,169926110309380,4126836768095315,
%U A246239 101114499262401970,2496432769621336865,62045482307629427354,1551083997228106913910,38976793037598171500920
%N A246239 Number of rooted trees with n nodes and 10-colored non-root nodes.
%H A246239 Alois P. Heinz, <a href="/A246239/b246239.txt">Table of n, a(n) for n = 0..500</a>
%H A246239 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 A246239 a(n) ~ c * d^n / n^(3/2), where d = 27.3718979186642404090999595957978919036..., c = 0.04017690459295003799582996890456677644... . - _Vaclav Kotesovec_, Aug 26 2014
%F A246239 G.f. A(x) satisfies: A(x) = x*exp(10*Sum_{k>=1} A(x^k)/k). - _Ilya Gutkovskiy_, Mar 20 2018
%p A246239 with(numtheory):
%p A246239 a:= proc(n) option remember; `if`(n<2, n, (add(add(d*
%p A246239       a(d), d=divisors(j))*a(n-j)*10, j=1..n-1))/(n-1))
%p A246239     end:
%p A246239 seq(a(n), n=0..25);
%t A246239 a[n_] := a[n] = If[n<2, n, Sum[Sum[d*a[d], {d, Divisors[j]}]*a[n-j]*10, {j, 1, n-1}]/(n-1)];
%t A246239 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Feb 23 2019, from Maple *)
%Y A246239 Column k=10 of A242249.
%K A246239 nonn
%O A246239 0,3
%A A246239 _Alois P. Heinz_, Aug 19 2014