OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..350
FORMULA
G.f. A(x) satisfies:
(1) A(x) = 1 + x*d/dx[x*A(x)^3],
(2) [x^n] exp( x*A(x)^3 ) * (n + 1 - A(x)) = 0 for n > 0,
(3) [x^n] exp( n * x*A(x)^3 ) * (2 - A(x)) = 0 for n > 0. - Paul D. Hanna, May 27 2018
From Vaclav Kotesovec, Oct 23 2020: (Start)
a(n) ~ c * 3^n * n! * n^(2/3), where c = 0.2509528330393045762351289...
a(n) ~ A113663(n)/3. (End)
a(0) = 1; a(n) = n * Sum_{i=0..n-1} Sum_{j=0..n-i-1} a(i) * a(j) * a(n-i-j-1). - Ilya Gutkovskiy, Jul 25 2021
PROG
(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=1+x*deriv(x*A^3)); polcoeff(A, n, x)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 04 2005
STATUS
approved