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%I #25 Mar 19 2023 14:15:12
%S 1,-2,-4,8,16,-32,-64,128,256,-512,-1024,2048,4096,-8192,-16384,32768,
%T 65536,-131072,-262144,524288,1048576,-2097152,-4194304,8388608,
%U 16777216,-33554432,-67108864,134217728,268435456,-536870912,-1073741824,2147483648,4294967296,-8589934592
%N Hankel transform of g.f. 1/sqrt(1+4x^2).
%C Hankel transform of e.g.f. Bessel_I(0,2*sqrt(-1)*x) or (1,0,-2,0,6,0,-20,...).
%C Hankel transform of Sum{k=0..n} (-1)^(n-k)*C(n,k)^2.
%C Hankel transform of A098331.
%C Hankel transform of A082590. - _Paul Barry_, Apr 26 2009
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,-4).
%F G.f.: (1-2*x)/(1+4*x^2); a(n) = 2^n*(cos(Pi*(n+1)/2)+sin(Pi*(n+1)/2)).
%F a(0)=1, a(1)=-2, a(n)=-4*a(n-2). - _Harvey P. Dale_, Oct 12 2011
%F a(n) = ( 2*i^(n+1) )^n, where i=sqrt(-1). - _Bruno Berselli_, Oct 12 2011
%F E.g.f.: cos(2*x) - sin(2*x). - _Arkadiusz Wesolowski_, Aug 31 2012
%t LinearRecurrence[{0,-4},{1,-2},40] (* or *) CoefficientList[ Series[ (1-2x)/(1+4x^2),{x,0,40}],x] (* _Harvey P. Dale_, Oct 12 2011 *)
%Y Cf. A082590, A098331.
%K sign,easy
%O 0,2
%A _Paul Barry_, Jun 17 2006
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