%I A120617
%S A120617 1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,
%T A120617 262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,
%U A120617 134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592
%V A120617 1,-2,-4,8,16,-32,-64,128,256,-512,-1024,2048,4096,-8192,-16384,32768,
               65536,-131072,
%W A120617 -262144,524288,1048576,-2097152,-4194304,8388608,16777216,-33554432,-67108864,
%X A120617 134217728,268435456,-536870912,-1073741824,2147483648,4294967296,-8589934592
%N A120617 Hankel transform of g.f. 1/sqrt(1+4x^2).
%C A120617 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.
%C A120617 Hankel transform of A082590. [From Paul Barry (pbarry(AT)wit.ie), Apr 
               26 2009]
%F A120617 G.f.: (1-2x)/(1+4x^2); a(n)=2^n*(cos(pi*(n+1)/2)+sin(pi*(n+1)/2))
%Y A120617 Sequence in context: A084633 A122803 A000079 this_sequence A050732 A138815 
               A103662
%Y A120617 Adjacent sequences: A120614 A120615 A120616 this_sequence A120618 A120619 
               A120620
%K A120617 easy,sign
%O A120617 0,2
%A A120617 Paul Barry (pbarry(AT)wit.ie), Jun 17 2006