A134762 a(n) = 3*A000984(n) - 2.

1, 4, 16, 58, 208, 754, 2770, 10294, 38608, 145858, 554266, 2116294, 8112466, 31201798, 120349798, 465352558, 1803241168, 7000818658, 27225405898, 106035791398, 413539586458, 1614773623318, 6312296891158, 24700292182798, 96742811049298, 379231819313254

Offset

0,2

Comments

Second inverse binomial transform of the sequence = A134763, (same as a(n) but with interpolated two's).

Links

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

Formula

G.f.: 3/sqrt(1-4*x) - 2/(1-x). - Sergei N. Gladkovskii, Nov 21 2013

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

a(n) = 3*(n+1)*A000108(n) - 2.

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

E.g.f.: 3*exp(2*x)*BesselI(0, 2*x) - 2*exp(x). (End)

Mathematica

Table[3*Binomial[2*n, n]-2, {n, 0, 40}] (* G. C. Greubel, May 28 2024 *)

Prog

(PARI) a(n) = 3*binomial(2*n, n) - 2; \\ Michel Marcus, Nov 22 2013
(Magma) [3*(n+1)*Catalan(n)-2: n in [0..40]]; // G. C. Greubel, May 28 2024
(SageMath) [3*binomial(2*n, n) -2 for n in range(41)] # G. C. Greubel, May 28 2024

Crossrefs

Cf. A000108, A000984, A134758, A134759, A134760, A134761, A134763, A134770, A134771.

Sequence in context: A180143 A224128 A123893 * A207276 A047123 A297096

Adjacent sequences: A134759 A134760 A134761 * A134763 A134764 A134765

Keyword

nonn

Author

Gary W. Adamson, Nov 09 2007

Extensions

More terms from Michel Marcus, Nov 22 2013

Status

approved