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 A027951 #17 Sep 08 2022 08:44:49
%S A027951 1,8,129,967,4950,20175,70954,226007,672959,1914166,5280288,14275838,
%T A027951 38102976,100888126,265838881,698489013,1832277574,4802042229,
%U A027951 12578921258,32941567397,86254888591,225835057708,591265802288,1547982265500,4052706300752
%N A027951 a(n) = T(2n,n+3), T given by A027948.
%H A027951 Colin Barker, <a href="/A027951/b027951.txt">Table of n, a(n) for n = 3..1000</a>
%H A027951 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (10,-43,105,-161,161,-105,43,-10,1).
%F A027951 G.f.: x^3*(1 -2*x +92*x^2 -84*x^3 +148*x^4 -162*x^5 +105*x^6 -43*x^7 +10*x^8 -x^9)/((1-x)^7*(1-3*x+x^2)). - _Colin Barker_, Nov 19 2014
%F A027951 From _G. C. Greubel_, Sep 29 2019: (Start)
%F A027951 a(n) = Sum_{j=0..n-3} binomial(2*n-j, j+7), with a(3) = 1 for n >= 3.
%F A027951 a(n) = Fibonacci(2*n+8) - (8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90 for n >= 4. (End)
%p A027951 with(combinat); seq(`if`(n=3,1, fibonacci(2*n+8) -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90), n=3..40); # _G. C. Greubel_, Sep 29 2019
%t A027951 CoefficientList[Series[(x^9 -10x^8 +43x^7 -105x^6 +162x^5 -148x^4 +84x^3 -92x^2 +2x -1)/((x-1)^7(x^2-3x+1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 20 2014 *)
%t A027951 Table[If[n==3, 1, Fibonacci[2*n+8] -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90], {n,3,40}] (* _G. C. Greubel_, Sep 29 2019 *)
%o A027951 (PARI) Vec(x^3*(x^9-10*x^8+43*x^7-105*x^6+162*x^5-148*x^4+84*x^3-92*x^2 +2*x-1)/((x-1)^7*(x^2-3*x+1)) + O(x^40)) \\ _Colin Barker_, Nov 19 2014
%o A027951 (PARI) vector(40, n, my(m=n+2); if(m==3, 1, fibonacci(2*m+8) -(8*m^6 -12*m^5 +110*m^4 +255*m^3 +872*m^2 +1827*m +1890)/90) ) \\ _G. C. Greubel_, Sep 29 2019
%o A027951 (Magma) [1] cat [Fibonacci(2*n+8) -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90: n in [4..40]]; // _G. C. Greubel_, Sep 29 2019
%o A027951 (Sage) [1]+[fibonacci(2*n+8) -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90 for n in (4..40)] # _G. C. Greubel_, Sep 29 2019
%o A027951 (GAP) Concatenation([1], List([4..40], n-> Fibonacci(2*n+8) -(8*n^6 -12*n^5 +110*n^4 +255*n^3 +872*n^2 +1827*n +1890)/90) ); # _G. C. Greubel_, Sep 29 2019
%Y A027951 Cf. A000045, A027948.
%K A027951 nonn,easy
%O A027951 3,2
%A A027951 _Clark Kimberling_
%E A027951 More terms from _Colin Barker_, Nov 19 2014