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Expansion of e.g.f. sqrt((1+2*x)/(1+4*x)).
1

%I #13 May 09 2022 00:09:20

%S 1,-1,7,-75,1089,-20025,446535,-11715795,353743425,-12084751665,

%T 460905128775,-19414191656475,895154327661825,-44844879530075625,

%U 2425592881954016775,-140881250370301315875,8745197742014671562625,-577792180264444615094625,40483044280613870034474375

%N Expansion of e.g.f. sqrt((1+2*x)/(1+4*x)).

%H Vincenzo Librandi, <a href="/A127190/b127190.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f.: sqrt((1+2*x)/(1+4*x)).

%F D-finite with recurrence: a(n) +(6*n-5)*a(n-1) +8*(n-1)*(n-2)*a(n-2)=0. - _R. J. Mathar_, Jan 24 2020

%t With[{nn=20},CoefficientList[Series[Sqrt[(1+2x)/(1+4x)],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 23 2014 *)

%K sign

%O 0,3

%A _N. J. A. Sloane_, Mar 26 2007