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 A100087 #22 Jul 08 2022 08:20:28
%S A100087 1,2,4,10,24,60,148,370,920,2300,5736,14340,35808,89520,223668,559170,
%T A100087 1397496,3493740,8732920,21832300,54575888,136439720,341082504,
%U A100087 852706260,2131706864,5329267160,13322959888,33307399720,83267756400,208169391000,520420803060,1301052007650
%N A100087 Expansion of x/(sqrt(1-4*x^2) + x - 1).
%C A100087 Inverse Chebyshev transform of (1-x^2)/((1-2*x)*(1+x^2)), the g.f. of A100088, under the mapping g(x) -> (1/sqrt(1-4*x^2))*g(x*c(x^2)) where c(x) is the g.f. of the Catalan numbers A000108. Equivalently, its image under the Chebyshev map A(x) -> ((1-x^2)/(1+x^2))*A(x/(1+x^2)) is A100088.
%C A100087 Transform of 1/(1-2*x) under the mapping g(x) -> g(x*c(x^2)). - _Paul Barry_, Jan 17 2005
%H A100087 Vincenzo Librandi, <a href="/A100087/b100087.txt">Table of n, a(n) for n = 0..1000</a>
%F A100087 a(n) = Sum_{k=0..floor(n/2)} C(n, k)*(3*2^(n-2*k) + 2*cos(Pi*(n-2*k)/2) + 4*sin(Pi*(n-2*k)/2))/5.
%F A100087 a(n) = Sum_{k=0..floor(n/2)} C(n, k)*A100088(n-2*k).
%F A100087 a(n) = Sum_{k=0..n} k*C(n-1,(n-k)/2)*(1 + (-1)^(n-k))*2^k/(n+k). - _Paul Barry_, Jan 17 2005
%F A100087 D-finite with recurrence: 4*n*a(n) + 2*(2*n-7)*a(n-1) - (51*n-83)*a(n-2) - 8*(2*n-13)*a(n-3) + 140*(n-4)*a(n-4) = 0. - _R. J. Mathar_, Nov 22 2012
%F A100087 a(n) ~ 3*5^(n-1)/2^n. - _Vaclav Kotesovec_, Dec 06 2012
%t A100087 CoefficientList[Series[x/(Sqrt[1-4*x^2]+x-1), {x, 0, 50}], x] (* _Vaclav Kotesovec_, Dec 06 2012 *)
%o A100087 (PARI) my(x='x+O('x^66)); Vec(x/(sqrt(1-4*x^2)+x-1)) \\ _Joerg Arndt_, May 12 2013
%o A100087 (Magma) R<x>:=PowerSeriesRing(Rationals(), 50); Coefficients(R!( x/(Sqrt(1-4*x^2) +x-1) )); // _G. C. Greubel_, Jul 08 2022
%o A100087 (SageMath)
%o A100087 @CachedFunction
%o A100087 def A100067(n): return sum( binomial(n,k)*2^(n-2*k) for k in (0..(n//2)) )
%o A100087 def A100087(n): return (3/5)*A100067(n) + (1/5)*((1+(-1)^n) -2*I*(1-(-1)^n))*I^n*(-1)^floor(n/2)*binomial(n-1, floor(n/2))
%o A100087 [A100087(n) for n in (0..60)] # _G. C. Greubel_, Jul 08 2022
%Y A100087 Cf. A000108, A100067, A100088.
%K A100087 easy,nonn
%O A100087 0,2
%A A100087 _Paul Barry_, Nov 03 2004