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A052772 Number of rooted identity trees with n nodes and 4-colored non-root nodes.

%I A052772 #24 Apr 13 2019 22:19:31
%S A052772 0,1,4,22,156,1193,9748,82916,727088,6524084,59620732,552970626,
%T A052772 5191935808,49252903050,471358286352,4545310993994,44121116086052,
%U A052772 430777978197156,4227634212037728,41680927531643928,412638233333973820,4100336181515969163,40882494461218775272
%N A052772 Number of rooted identity trees with n nodes and 4-colored non-root nodes.
%C A052772 Previous name was: A simple grammar.
%H A052772 Alois P. Heinz, <a href="/A052772/b052772.txt">Table of n, a(n) for n = 0..1000</a>
%H A052772 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=729">Encyclopedia of Combinatorial Structures 729</a>
%F A052772 a(n) ~ c * d^n / n^(3/2), where d = 10.68849275496965245845204879846824293047921245695819153804780100052532088..., c = 0.097992887955331161579155538221616838965194192139... . - _Vaclav Kotesovec_, Feb 24 2015
%F A052772 From _Ilya Gutkovskiy_, Apr 13 2019: (Start)
%F A052772 G.f. A(x) satisfies: A(x) = x*exp(4*Sum_{k>=1} (-1)^(k+1)*A(x^k)/k).
%F A052772 G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x * Product_{n>=1} (1 + x^n)^(4*a(n)). (End)
%p A052772 spec := [S,{S=Prod(Z,B,B,B,B),B=PowerSet(S)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
%Y A052772 Column k=4 of A255517.
%K A052772 easy,nonn
%O A052772 0,3
%A A052772 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052772 New name from _Vaclav Kotesovec_, Feb 24 2015