OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..312
FORMULA
E.g.f. satisfies: A(x) = 1 + Integral [1 + x*A(x)^4] dx.
a(n) ~ n^(n-1/6) * sqrt(2*Pi) / (3^(1/3) * GAMMA(1/3) * exp(n) * r^(n+2/3)), where r = 0.52731343741213... (multiplicative constant is conjectured, holds 14 decimal places). - Vaclav Kotesovec, Feb 24 2014
EXAMPLE
E.g.f.: A(x) = 1 + x + x^2/2! + 8*x^3/3! + 48*x^4/4! + 368*x^5/5! +...
A(x)^4 = 1 + 4*x + 16*x^2/2! + 92*x^3/3! + 780*x^4/4! + 7832*x^5/5! +...
x*A(x)^4 = x + 8*x^2/2! + 48*x^3/3! + 368*x^4/4! + 3900*x^5/5! +...
A'(x) = 1 + x + 8*x^2/2! + 48*x^3/3! + 368*x^4/4! + 3900*x^5/5! +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(1+x*(A+x*O(x^n))^4)); n!*polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 10 2008
STATUS
approved