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 A027980 #17 Sep 08 2022 08:44:50
%S A027980 1,13,48,176,580,1844,5667,17047,50404,147090,424686,1215528,3453733,
%T A027980 9752641,27393240,76587284,213260152,591707612,1636514439,4513276555,
%U A027980 12414985996,34071252918,93305816418,255027755856,695815086025,1895348847349,5154987856512,14000952578552
%N A027980 a(n) = Sum_{k=0..n-1} T(n,k)*T(n,2n-k), T given by A027960.
%H A027980 G. C. Greubel, <a href="/A027980/b027980.txt">Table of n, a(n) for n = 0..1000</a>
%H A027980 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-5,5,-1).
%F A027980 G.f.: (1 +8*x -12*x^2 +6*x^3)/ ((1+x)*(1-3*x+x^2)^2). - _Colin Barker_, Nov 25 2014
%F A027980 a(n) = (n+1)*Lucas(2*n) - Fibonacci(2*n+1) - (-1)^n. - _G. C. Greubel_, Oct 01 2019
%p A027980 with(combinat); f:=fibonacci; seq((n+1)*(f(2*n+3) + f(2*n+1)) - f(2*n+1) -(-1)^n, n=0..40); # _G. C. Greubel_, Oct 01 2019
%t A027980 Table[(n+1)*LucasL[2*n+2] -Fibonacci[2*n+1] -(-1)^n, {n,0,40}] (* _G. C. Greubel_, Oct 01 2019 *)
%o A027980 (PARI) vector(41, n, f=fibonacci; n*(f(2*n+1) + f(2*n-1)) - f(2*n-1) + (-1)^n) \\ _G. C. Greubel_, Oct 01 2019
%o A027980 (Magma) [(n+1)*Lucas(2*n+2) - Fibonacci(2*n+1) -(-1)^n: n in [0..40]]; // _G. C. Greubel_, Oct 01 2019
%o A027980 (Sage) [(n+1)*lucas_number2(2*n+2,1,-1) - fibonacci(2*n+1) -(-1)^n for n in (0..40)] # _G. C. Greubel_, Oct 01 2019
%o A027980 (GAP) List([0..40], n-> (n+1)*Lucas(1,-1,2*n+2)[2] - Fibonacci(2*n+1) -(-1)^n); # _G. C. Greubel_, Oct 01 2019
%Y A027980 Cf. A000032, A000045, A027960.
%K A027980 nonn
%O A027980 0,2
%A A027980 _Clark Kimberling_
%E A027980 Terms a(24) onward added by _G. C. Greubel_, Oct 01 2019