%I #13 Aug 11 2014 06:44:10
%S 1,1,6,135,4811,229670,13511540,936653101,74430448182,6655256746640,
%T 660714896623941,72089721075875610,8574673889180457825,
%U 1104434190128518376048,153171642055215265173031,22761836879580561483967360,3608810191272206965533932200
%N G.f. satisfies: A(x)^2 = x + A(x*A(x)^7).
%C In general, if g.f. satisfies: A(x)^2 = x + A(x*A(x)^q), q > 1, then a(n) ~ c(q) * q^n * n^(n - 1/q + (1/2 - 3/(2*q))*log(2)) / (exp(n) * log(2)^n), where c(q) is a constant independent on n.
%H Vaclav Kotesovec, <a href="/A241999/b241999.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) ~ c * 7^n * n^(n - 1/7 + 2/7*log(2)) / (exp(n) * log(2)^n), where c = 0.1428317047130699...
%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^7) - 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), A241998 (q=6).
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Aug 11 2014