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A120617 Hankel transform of g.f. 1/sqrt(1+4x^2). 5
1, -2, -4, 8, 16, -32, -64, 128, 256, -512, -1024, 2048, 4096, -8192, -16384, 32768, 65536, -131072, -262144, 524288, 1048576, -2097152, -4194304, 8388608, 16777216, -33554432, -67108864, 134217728, 268435456, -536870912, -1073741824, 2147483648, 4294967296, -8589934592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform of e.g.f. Bessel_I(0,2*sqrt(-1)*x) or (1,0,-2,0,6,0,-20,...). Hankel transform of sum{k=0..n, (-1)^(n-k)*C(n,k)^2}. Hankel transform of A098331.

Hankel transform of A082590. - Paul Barry, Apr 26 2009

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (0,-4)

FORMULA

G.f.: (1-2*x)/(1+4*x^2); a(n)=2^n*(cos(pi*(n+1)/2)+sin(pi*(n+1)/2))

a(0)=1, a(1)=-2, a(n)=-4*a(n-2). - Harvey P. Dale, Oct 12 2011

a(n) = ( 2*i^(n+1) )^n, where i=sqrt(-1). - Bruno Berselli, Oct 12 2011

E.g.f.: cos(2*x) - sin(2*x). - Arkadiusz Wesolowski, Aug 31 2012

MATHEMATICA

LinearRecurrence[{0, -4}, {1, -2}, 40] (* or *) CoefficientList[ Series[ (1-2x)/(1+4x^2), {x, 0, 40}], x] (* Harvey P. Dale, Oct 12 2011 *)

CROSSREFS

Sequence in context: * A131577 A155559 A171449 A122803 A274867 A274866

Adjacent sequences:  A120614 A120615 A120616 * A120618 A120619 A120620

KEYWORD

sign,easy

AUTHOR

Paul Barry, Jun 17 2006

STATUS

approved

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Last modified June 25 20:26 EDT 2017. Contains 288730 sequences.