OFFSET
0,2
COMMENTS
Hankel transform is A144708.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 3/sqrt(1-4*x) - 2;
a(n) = 3*binomial(2*n, n) - 2*0^n.
From Philippe Deléham, Oct 30 2008: (Start)
D-finite with recurrence: n*a(n) = 2*(2*n-1)*a(n-1). - R. J. Mathar, Nov 30 2012
E.g.f.: -2 + 3*exp(2*x)*BesselI(0, 2*x). - G. C. Greubel, Jun 16 2022
MATHEMATICA
Table[3*Binomial[2n, n] -2*Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Jun 16 2022 *)
PROG
(Magma) [n eq 0 select 1 else 3*(n+1)*Catalan(n): n in [0..40]]; // G. C. Greubel, Jun 16 2022
(SageMath) [3*binomial(2*n, n) -2*bool(n==0) for n in (0..40)] # G. C. Greubel, Jun 16 2022
(PARI) a(n) = if(n, 3*binomial(2*n, n), 1) \\ Charles R Greathouse IV, Oct 23 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 19 2008
STATUS
approved