%I #10 Sep 08 2022 08:45:29
%S 1,1,-5,39,-423,5985,-105885,2269575,-57475215,1684565505,
%T -56176247925,2101511463975,-87163146984375,3969387329933025,
%U -196863216968342925,10560219055989978375,-609129291476291961375,37591662102746977850625,-2471292534125033454961125
%N E.g.f.: sqrt((1+4*x)/(1+2*x)).
%F D-finite with recurrence: a(n) +(6*n-7)*a(n-1) +8*(n-1)*(n-2)*a(n-2)=0. - _R. J. Mathar_, Jan 25 2020
%t With[{nn=20}, CoefficientList[Series[Sqrt[(1 + 4 x) / (1 + 2 x)], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Jan 26 2020 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Sqrt((1+4*x)/(1+2*x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _Vincenzo Librandi_, Jan 26 2020
%K sign
%O 0,3
%A _N. J. A. Sloane_, Mar 26 2007