OFFSET
1,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Nickolas Hein and Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.
FORMULA
G.f.: x^2*(1-3*x+sqrt(1-2*x-3*x^2))/((1-3*x)*(3*x-1+sqrt(1-2*x-3*x^2))). - amended by Georg Fischer, Apr 09 2020
D-finite with recurrence: (-n+1)*a(n) +(5*n-8)*a(n-1) +3*(-n+1)*a(n-2) +9*(-n+4)*a(n-3)=0. - R. J. Mathar, Jan 28 2020
a(n) ~ 3^(n-2) * (1 + sqrt(3/(Pi*n))). - Vaclav Kotesovec, Apr 09 2020
MATHEMATICA
Rest[CoefficientList[Series[x^2*(1-3*x+Sqrt[1-2*x-3*x^2])/((1-3*x)*(3x-1+Sqrt[1- 2*x-3*x^2])), {x, 0, 30}], x]] (* Harvey P. Dale, Jun 03 2012; Georg Fischer, Apr 09 2020 *)
PROG
(PARI) seq(n)={my(p=sqrt(1-2*x-3*x^2 + O(x*x^n))); Vec(x^2*(1-3*x+p)/((1-3*x)*(3*x-1+p)))} \\ Andrew Howroyd, Apr 09 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Jun 03 2012
STATUS
approved