OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: A(x) = sum(n>=0, Catalan(n+1)*x^n) + x^2*A(x)^4, where Catalan(n)=(2n)!/(n!*(n+1)!).
From Vaclav Kotesovec, Oct 10 2020: (Start)
G.f.: A(x) = (1 - Sqrt[1-4*x] - 2*x)/(2*x^2) + x^2*A(x)^4.
a(n) ~ sqrt(11) * 3^(15/2 + 3*n) / ((8 + 3*sqrt(3) + 4*sqrt(4 + 3*sqrt(3))) * sqrt((2519 + 528*sqrt(3) + 2*sqrt(1484692 + 881529*sqrt(3))) * Pi) * n^(3/2) * 2^(2*n + 5/2) * (-32 - 18*sqrt(3) + sqrt(1996 + 1233*sqrt(3)))^(n+2)). (End)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 02 2003
STATUS
approved