STATUS
editing
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
editing
approved
(PARI) a(n) = if(n, 3*binomial(2*n, n), 1) \\ Charles R Greathouse IV, Oct 23 2023
approved
editing
proposed
approved
editing
proposed
Central coefficients of Pascal-like the triangle A132047.
reviewed
editing
proposed
reviewed
editing
proposed
G. C. Greubel, <a href="/A144706/b144706.txt">Table of n, a(n) for n = 0..1000</a>
G.f.: 3/sqrt(1-4x4*x) - 2;
a(n) = 3*binomial(2n,2*n, n) - 2*0^n.
From Philippe Deléham, Oct 30 2008: (Start)
a(n) = Sum_{k=0..n} A039599(n,k)*A010686(k) = Sum_{k=0..n} A106566(n,k)*A082505(k+1). - _Philippe Deléham_, Oct 30 2008
a(n) = Sum_{k=0..n} A106566(n,k)*A082505(k+1). (End)
D-finite with recurrence: n*a(n) + = 2*(-2*n+-1)*a(n-1) = 0. - R. J. Mathar, Nov 30 2012
E.g.f.: -2 + 3*exp(2*x)*BesselI(0, 2*x). - G. C. Greubel, Jun 16 2022
Table[3*Binomial[2n, n] -2*Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Jun 16 2022 *)
(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
approved
editing
D-finite with recurrence: n*a(n) + 2*(-2*n+1)*a(n-1) = 0. - R. J. Mathar, Nov 30 2012
proposed
approved