Voozh

A241999

G.f. satisfies: A(x)^2 = x + A(x*A(x)^7).

1, 1, 6, 135, 4811, 229670, 13511540, 936653101, 74430448182, 6655256746640, 660714896623941, 72089721075875610, 8574673889180457825, 1104434190128518376048, 153171642055215265173031, 22761836879580561483967360, 3608810191272206965533932200

(list; graph; refs; listen; history; text; internal format)

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

Cf. A240996 (q=2), A240999 (q=3), A241996 (q=4), A241997 (q=5), A241998 (q=6).

Sequence in context: A096756 A386415 A356505 * A333005 A013299 A013295

Adjacent sequences: A241996 A241997 A241998 * A242000 A242001 A242002