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%I #7 Aug 24 2017 08:03:49
%S 1,1,6,66,1016,19596,447312,11686008,341966304,11044539840,
%T 389511815136,14879686213728,611795661826176,26934556130346880,
%U 1264203675152355840,63023836596988857216,3326204117173583906304,185302040367551696870400,10868134346437165639956480
%N G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x) )^3.
%H Vaclav Kotesovec, <a href="/A211824/b211824.txt">Table of n, a(n) for n = 0..250</a>
%F G.f. satisfies: A(x) = 1 + x*(A(x) + x*A'(x))^3.
%F a(n) ~ c * 3^n * n! * n^(4/3), where c = 0.1005380575409567... - _Vaclav Kotesovec_, Aug 24 2017
%e G.f.: A(x) = 1 + x + 6*x^2 + 66*x^3 + 1016*x^4 + 19596*x^5 + 447312*x^6 +...
%e Related expansions:
%e d/dx x*A(x) = 1 + 2*x + 18*x^2 + 264*x^3 + 5080*x^4 + 117576*x^5 +...
%e A'(x) = 1 + 12*x + 198*x^2 + 4064*x^3 + 97980*x^4 + 2683872*x^5 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x*deriv(x*A)^3);polcoeff(A,n)}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A112915, A211825, A211826.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Apr 21 2012
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