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 A087169 #29 Jun 10 2022 06:16:20
%S A087169 1,-2,1,13,-74,253,-599,718,1801,-15467,61126,-166427,282001,87838,
%T A087169 -2977199,14095453,-43682474,91553293,-64624199,-500858642,3085911001,
%U A087169 -10921827227,26835937126,-35883240587,-62107231199,633485321278,-2608461525599,7340939736493,-13228544952074
%N A087169 Expansion of (1 + 3*x)/(1 + 5*x + 9*x^2).
%C A087169 For positive n, a(n) equals 3^n times the permanent of the (2n) X (2n) tridiagonal matrix with 1/sqrt(3)'s along the main diagonal, and i's along the superdiagonal and the subdiagonal (where i is the imaginary unit). - _John M. Campbell_, Jul 08 2011
%H A087169 G. C. Greubel, <a href="/A087169/b087169.txt">Table of n, a(n) for n = 0..1000</a>
%H A087169 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-5,-9).
%F A087169 G.f.: (1 + 3*x)/(1 + 5*x + 9*x^2).
%F A087169 a(n) = -5*a(n-1) - 9*a(n-2), a(0)=1, a(1)=-2.
%F A087169 a(n) = Sum_{k=0..n} binomial(n+k,2*k)*(-3)^(n-k).
%F A087169 a(n) = (-3)^n*( ChebyshevU(n, 5/6) - ChebyshevU(n-1, 5/6) ). - _G. C. Greubel_, Jun 09 2022
%t A087169 CoefficientList[Series[(1+3x)/(1+5x+9x^2), {x, 0, 30}], x]
%t A087169 LinearRecurrence[{-5,-9},{1,-2},50] (* _Harvey P. Dale_, Mar 24 2021 *)
%o A087169 (Magma) [n le 2 select (-1)^(n-1)*n else -5*Self(n-1) - 9*Self(n-2): n in [1..51]]; // _G. C. Greubel_, Jun 09 2022
%o A087169 (SageMath)
%o A087169 def A087169(n): return (-3)^n*(chebyshev_U(n, 5/6) - chebyshev_U(n-1, 5/6))
%o A087169 [A087169(n) for n in (0..50)] # _G. C. Greubel_, Jun 09 2022
%Y A087169 Cf. A190970.
%K A087169 easy,sign
%O A087169 0,2
%A A087169 Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2003