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 A156857 #10 Jan 28 2022 16:30:51
%S A156857 1,0,-9,10,45,-108,-125,702,-135,-3320,4239,11250,-31931,-18180,
%T A156857 165915,-92762,-651375,1101168,1747495,-6710310,-694179,30182500,
%U A156857 -28394829,-101934450,229069225,203510232,-1198850625,364506562,4767453045
%N A156857 Expansion of (1+2*x)/(1+x+4*x^2)^2.
%C A156857 Hankel transform of A091526.
%H A156857 G. C. Greubel, <a href="/A156857/b156857.txt">Table of n, a(n) for n = 0..1000</a>
%H A156857 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-9,-8,-16).
%F A156857 G.f.: (1 +2*x)/(1 +2*x +9*x^2 +8*x^3 +16*x^4).
%F A156857 a(n) = (-2)*Sum_{j=0..n} ChebyshevU(n-j, 1/4)*(ChebyshevU(j, 1/4) - ChebyshevU(j-1, 1/4)). - _G. C. Greubel_, Jan 28 2022
%t A156857 LinearRecurrence[{-2,-9,-8,-16}, {1,0,-9,10}, 41] (* or *)
%t A156857 A156857[n_]:= (-2)^n*Sum[ChebyshevU[n-j, 1/4]*(ChebyshevU[j, 1/4] - ChebyshevU[j-1, 1/4]), {j,0,n}];
%t A156857 Table[A156857[n], {n, 0, 40}] (* _G. C. Greubel_, Jan 28 2022 *)
%o A156857 (Magma) I:=[1,0,-9,10]; [n le 4 select I[n] else (-1)*(2*Self(n-1) +9*Self(n-2) +8*Self(n-3) +16*Self(n-4)): n in [1..41]]; // _G. C. Greubel_, Jan 28 2022
%o A156857 (Sage)
%o A156857 def A156857(n): return (-2)^n*sum( chebyshev_U(n-j, 1/4)*(chebyshev_U(j, 1/4) - chebyshev_U(j-1, 1/4)) for j in (0..n))
%o A156857 [A156857(n) for n in (0..40)] # _G. C. Greubel_, Jan 28 2022
%Y A156857 Cf. A091526, A106853.
%K A156857 easy,sign
%O A156857 0,3
%A A156857 _Paul Barry_, Feb 17 2009