OFFSET
0,3
COMMENTS
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.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..250
FORMULA
a(n) ~ c * 7^n * n^(n - 1/7 + 2/7*log(2)) / (exp(n) * log(2)^n), where c = 0.1428317047130699...
PROG
(PARI) {a(n)=local(A=[1, 1], Ax); for(i=1, n, A=concat(A, 0); Ax=Ser(A);
A[#A]=Vec(1+subst(Ax, x, x*Ax^7) - Ax^2)[#A]); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 11 2014
STATUS
approved