%I #9 Aug 11 2014 06:35:25

%S 1,1,5,95,2865,115995,5795546,341588686,23099712021,1759081180848,

%T 148827977847297,13846375810530924,1405013226803228823,

%U 154447381376266478808,18287299416725063983915,2320814090889444342775833,314320342934125785370051303

%N G.f. satisfies: A(x)^2 = x + A(x*A(x)^6).

%H Vaclav Kotesovec, <a href="/A241998/b241998.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) ~ c * 6^n * n^(n - 1/6 + 1/4*log(2)) / (exp(n) * log(2)^n), where c = 0.1671159774327212...

%o (PARI) {a(n)=local(A=[1, 1], Ax); for(i=1, n, A=concat(A, 0); Ax=Ser(A);

%o A[#A]=Vec(1+subst(Ax, x, x*Ax^6) - Ax^2)[#A]); A[n+1]}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A240996 (q=2), A240999 (q=3), A241996 (q=4), A241997 (q=5), A241999 (q=7).

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Aug 11 2014