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%I #11 Sep 03 2021 12:22:27
%S 1,1,-2,-2,6,6,-20,-20,70,70,-252,-252,924,924,-3432,-3432,12870,
%T 12870,-48620,-48620,184756,184756,-705432,-705432,2704156,2704156,
%U -10400600,-10400600,40116600,40116600,-155117520,-155117520
%N Expansion of (1+x)/sqrt(1+4x^2).
%C Hankel transform is A128056. Binomial transform is A128058. Unsigned version is A128014.
%F a(n)=(-1)^C(n,2)*(C(n,n/2)*(1+(-1)^n)/2+C(n-1,(n-1)/2)*(1-(-1)^n)/2);
%F Conjecture: n*(5*n-9)*a(n) +4*a(n-1) +4*(5*n-4)*(n-2)*a(n-2)=0. - _R. J. Mathar_, Dec 02 2014
%F D-finite with recurrence: n*a(n) +(n-2)*a(n-1) +4*(n-1)*a(n-2) +4*(n-3)*a(n-3)=0. - _R. J. Mathar_, Dec 02 2014
%t CoefficientList[Series[(1+x)/Sqrt[1+4x^2],{x,0,40}],x] (* _Harvey P. Dale_, May 12 2015 *)
%Y Cf. A000984.
%K easy,sign
%O 0,3
%A _Paul Barry_, Feb 13 2007