OFFSET
0,3
COMMENTS
a(n)=K(3,3; n)/3 with K(a,b; n) defined in a comment to A068763.
LINKS
Fung Lam, Table of n, a(n) for n = 0..1000
FORMULA
a(n)=(3^n)*p(n, -2/3) with the row polynomials p(n, x) defined from array A068763.
a(n+1)= 3*sum(a(k)*a(n-k), k=0..n), n>=1, a(0)=1=a(1).
G.f.: (1-sqrt(1-12*x*(1-2*x)))/(6*x).
Recurrence: (n+1)*a(n) = 24*(2-n)*a(n-2) + 6*(2*n-1)*a(n-1). - Fung Lam, Mar 04 2014
a(n) ~ sqrt(6+6*sqrt(3)) * (6+2*sqrt(3))^n / (6*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 04 2014
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-12*x*(1-2*x)])/(6*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 04 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Mar 04 2002
STATUS
approved