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%I #10 Jan 30 2020 21:29:16
%S 1,2,-2,-2,10,-6,-42,102,82,-782,814,3854,-12454,-5014,98694,-142218,
%T -472158,1932258,19038,-14816994,27370410,64159962,-334154442,
%U 121279878,2418497010,-5523511086,-8914677362,61259567662,-44249714438
%N Expansion of (sqrt(1+2x+9x^2)+x-1)/(2x).
%C First column of A125694.
%C Hankel transform is (-2)^C(n+1, 2)*A001045(n+2).
%F a(n)=0^n+2*sum{k=0..floor((n-1)/2), C(n-1,2k)*C(k)*(-1)^(n-k-1)*2^k}, C(n)=A000108(n).
%F D-finite with recurrence: (n+1)*a(n) +(2*n-1)*a(n-1) +9*(n-2)*a(n-2)=0. - _R. J. Mathar_, Dec 02 2014
%t CoefficientList[Series[(Sqrt[1+2x+9x^2]+x-1)/(2x),{x,0,30}],x] (* _Harvey P. Dale_, Jul 25 2013 *)
%Y Cf. A091593.
%K easy,sign
%O 0,2
%A _Paul Barry_, Nov 30 2006, Dec 10 2008