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%I #18 Sep 08 2022 08:45:19
%S 1,1,5,9,5,-7,5,73,69,-295,-571,1321,4613,-4167,-32635,-1783,211141,
%T 200601,-1229243,-2468375,6117509,22557305,-21519611,-176980023,
%U -13664955,1234115673,1250908869,-7608051031,-16094268667,39424807225,153179607429,-139981878647,-1243776268859
%N Expansion of sqrt((1-x+8*x^2)/(1-x)^3).
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0509316">On the Integrality of n-th Roots of Generating Functions</a>, arXiv:math/0509316 [math.NT], 2005-2006.
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="https://doi.org/10.1016/j.jcta.2006.03.018">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%F D-finite with recurrence: n*a(n) +(-2*n+1)*a(n-1) +(9*n-25)*a(n-2) +4*(-2*n+5)*a(n-3)=0. - _R. J. Mathar_, Jan 24 2020
%t CoefficientList[Series[Sqrt[(1-x+8x^2)/(1-x)^3],{x,0,50}],x] (* _Harvey P. Dale_, Dec 24 2018 *)
%o (Magma) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(Sqrt((1-x+8*x^2)/(1-x)^3))); // _Vincenzo Librandi_, Jan 25 2020
%Y Square root of g.f. for A054552.
%K sign
%O 0,3
%A _N. J. A. Sloane_ and _Nadia Heninger_, Jun 28 2005