A134758 a(n) = A000984(n) + n.

1, 3, 8, 23, 74, 257, 930, 3439, 12878, 48629, 184766, 705443, 2704168, 10400613, 40116614, 155117535, 601080406, 2333606237, 9075135318, 35345263819, 137846528840, 538257874461, 2104098963742, 8233430727623, 32247603683124, 126410606437777, 495918532948130

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

G.f.: ((1-x)^2 + x*sqrt(1-4*x))/((1-x)^2*sqrt(1-4*x)). - Harvey P. Dale, Dec 10 2011

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

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

a(n) = (2*(2*n-1)*a(n-1) - (3*n^2 - 6*n + 2))/n. (End)

Mathematica

Table[Binomial[2n, n]+n, {n, 0, 40}] (* Harvey P. Dale, Dec 10 2011 *)

Prog

(Magma) [n+(n+1)*Catalan(n): n in [0..40]]; // G. C. Greubel, May 28 2024
(SageMath) [n+binomial(2*n, n) for n in range(41)] # G. C. Greubel, May 28 2024

Crossrefs

Cf. A000984, A134759, A134760, A134761, A134762, A134763, A134770, A134771.

Sequence in context: A124462 A047857 A101495 * A050511 A151405 A148778

Adjacent sequences: A134755 A134756 A134757 * A134759 A134760 A134761

Keyword

nonn

Author

Gary W. Adamson, Nov 09 2007

Extensions

More terms from Harvey P. Dale, Dec 10 2011

Status

approved