OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..250
FORMULA
G.f. satisfies: A(x) = 1 + x*(A(x) + x*A'(x))^3.
a(n) ~ c * 3^n * n! * n^(4/3), where c = 0.1005380575409567... - Vaclav Kotesovec, Aug 24 2017
EXAMPLE
G.f.: A(x) = 1 + x + 6*x^2 + 66*x^3 + 1016*x^4 + 19596*x^5 + 447312*x^6 +...
Related expansions:
d/dx x*A(x) = 1 + 2*x + 18*x^2 + 264*x^3 + 5080*x^4 + 117576*x^5 +...
A'(x) = 1 + 12*x + 198*x^2 + 4064*x^3 + 97980*x^4 + 2683872*x^5 +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*deriv(x*A)^3); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 21 2012
STATUS
approved