This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A104551 #16 Jan 02 2023 02:18:55
%S A104551 0,1,1,-1,-1,5,5,-15,-15,55,55,-197,-197,727,727,-2705,-2705,10165,
%T A104551 10165,-38455,-38455,146301,146301,-559131,-559131,2145025,2145025,
%U A104551 -8255575,-8255575,31861025,31861025,-123256495,-123256495,477823895,477823895,-1855782325,-1855782325,7219352975
%N A104551 Expansion of x/((1-x)*sqrt(1+4*x^2)).
%C A104551 A transformation of the Fibonacci numbers A000045 by the Riordan array (1/sqrt(1+4*x^2), (sqrt(1+4*x^2)-1)/(2*x)).
%H A104551 G. C. Greubel, <a href="/A104551/b104551.txt">Table of n, a(n) for n = 0..1000</a>
%F A104551 G.f.: x/((1-x)*sqrt(1+4*x^2)).
%F A104551 a(n) = Sum_{k=0..n} (sin(Pi*k/2)+cos(Pi*k)/2+1/2)*C(k-1,(k-1)/2)*(1-(-1)^k)/2.
%F A104551 D-finite with recurrence: (n-1)*a(n) = (n-1)*a(n-1) - 4*(n-2)*a(n-2) + 4*(n-2)*a(n-3). - _R. J. Mathar_, Feb 20 2015
%t A104551 CoefficientList[Series[x/((1-x)*Sqrt[1+4*x^2]), {x,0,40}], x] (* _G. C. Greubel_, Jan 01 2023 *)
%o A104551 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x/((1-x)*Sqrt(1+4*x^2)) )); // _G. C. Greubel_, Jan 01 2023
%o A104551 (SageMath)
%o A104551 def A104551_list(prec):
%o A104551 P.<x> = PowerSeriesRing(ZZ, prec)
%o A104551 return P( x/((1-x)*sqrt(1+4*x^2)) ).list()
%o A104551 A104551_list(40) # _G. C. Greubel_, Jan 01 2023
%Y A104551 Cf. A000045, A054108.
%K A104551 easy,sign
%O A104551 0,6
%A A104551 _Paul Barry_, Mar 14 2005