A166588 Partial sums of A097331; binomial transform of A166587.

1, 2, 2, 3, 3, 5, 5, 10, 10, 24, 24, 66, 66, 198, 198, 627, 627, 2057, 2057, 6919, 6919, 23715, 23715, 82501, 82501, 290513, 290513, 1033413, 1033413, 3707853, 3707853, 13402698, 13402698, 48760368, 48760368, 178405158, 178405158, 656043858

Offset

0,2

Comments

Hankel transform is A131713. The Hankel transform of the sequence 1,1,2,2,... is A128017(n+3). A155587 doubled.

Links

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

Formula

G.f.: (1+2x-sqrt(1-4x^2))/(2x(1-x))=((1+x^2*c(x^2))/(1-x)-1)/x, c(x) the g.f. of A000108.

a(n) = Sum_{k=0..n} C(n,k)*A166587(k).

Conjecture: (-n-1)*a(n) + (n+1)*a(n-1) + 4*(n-2)*a(n-2) + 4*(-n+2)*a(n-3) = 0. - R. J. Mathar, Nov 15 2012

a(n) ~ 2^(n+1/2) * (3-(-1)^n) / (3 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 08 2014

Mathematica

CoefficientList[Series[(1+2*x-Sqrt[1-4*x^2])/(2*x*(1-x)), {x, 0, 40}], x] (* Vaclav Kotesovec, Feb 08 2014 *)

Crossrefs

Sequence in context: A000358 A032244 A342654 * A277321 A262365 A063988

Adjacent sequences: A166585 A166586 A166587 * A166589 A166590 A166591

Keyword

easy,nonn

Author

Paul Barry, Oct 17 2009

Status

approved