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A166588 Partial sums of A097331; binomial transform of A166587. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A246998 A000358 A032244 * A277321 A262365 A063988

Adjacent sequences:  A166585 A166586 A166587 * A166589 A166590 A166591

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 17 2009

STATUS

approved

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)