A134759 a(n) = 2*A000984(n) - (n+1).

1, 2, 9, 36, 135, 498, 1841, 6856, 25731, 97230, 369501, 1410852, 5408299, 20801186, 80233185, 310235024, 1202160763, 4667212422, 18150270581, 70690527580, 275693057619, 1076515748858, 4208197927417, 16466861455176, 64495207366175, 252821212875478

Offset: 0

Author

Gary W. Adamson, Nov 09 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000108, A000984, A134758, A134760, A134761, A134762, A134763, A134770, A134771.

Programs

Magma

[(n+1)*(2*Catalan(n)-1): n in [0..40]]; // G. C. Greubel, May 28 2024

Mathematica

Table[2 Binomial[2n,n]-n-1,{n,0,30}] (* Harvey P. Dale, Aug 07 2023 *)

SageMath

[2*binomial(2*n,n) -(n+1) for n in range(41)] # G. C. Greubel, May 28 2024

Formula

From G. C. Greubel, May 28 2024: (Start)

a(n) = (n+1)*(2*A000108(n) - 1).

a(n) = (2*(2*n-1)*a(n-1) + 3*n*(n-1))/n.

G.f.: 2/sqrt(1-4*x) - 1/(1-x)^2.

E.g.f.: 2*exp(2*x)*BesselI(0, 2*x) - (1+x)*exp(x). (End)

Extensions

More terms from Harvey P. Dale, Aug 07 2023