A144706 - OEIS

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

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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