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%I #14 Aug 15 2014 10:23:37
%S 1,1,1,11,156,3291,88226,2875398,110100183,4841244682,240373761685,
%T 13302190764348,811959804656631,54199237928855551,3927985314859401651,
%U 307182890826521602838,25785326923948811144846,2312543296773573900444136,220690745096282461500094088
%N G.f. satisfies: A(x) = 1 - x + A(x)^3 - A(x*A(x)^4).
%H Vaclav Kotesovec, <a href="/A242008/b242008.txt">Table of n, a(n) for n = 0..340</a>
%F a(n) ~ c * 4^n * n^(n - 3/4 - 3/8*log(2)) / (exp(n) * (log(2))^n), where c = 0.137369844026491686111562...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A = 2*A - (1-x + A^3 - subst(A,x,x*A^4 +x*O(x^n))) );polcoeff(A,n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A242007 (q=3), A242009 (q=5).
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Aug 11 2014
%E Name corrected by _Vaclav Kotesovec_ and _Paul D. Hanna_, Aug 15 2014
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