A144706 Central coefficients of the triangle A132047.

1, 6, 18, 60, 210, 756, 2772, 10296, 38610, 145860, 554268, 2116296, 8112468, 31201800, 120349800, 465352560, 1803241170, 7000818660, 27225405900, 106035791400, 413539586460, 1614773623320

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)

a(n) = Sum_{k=0..n} A039599(n,k)*A010686(k).

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). - 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

Cf. A000108, A010686, A039599, A082505, A106566, A132047, A144708.

Sequence in context: A223468 A223211 A334330 * A074427 A034751 A200151

Adjacent sequences: A144703 A144704 A144705 * A144707 A144708 A144709

Keyword

easy,nonn

Author

Paul Barry, Sep 19 2008

Status

approved