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 A027944 #11 Sep 08 2022 08:44:49
%S A027944 1,37,376,2267,10220,38403,127921,392688,1140260,3189022,8699540,
%T A027944 23352118,62048869,163843187,431026972,1131463777,2966502032,
%U A027944 7772382641,20356549685,53305176134,139569431544,365416760764,956698453752,2504701077772,6557433205689,17167634170241
%N A027944 a(n) = T(2n+1, n+4), T given by A027935.
%H A027944 G. C. Greubel, <a href="/A027944/b027944.txt">Table of n, a(n) for n = 3..1000</a>
%H A027944 <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 A027944 From _G. C. Greubel_, Sep 28 2019: (Start)
%F A027944 a(n) = Sum_{j=0..n-3} binomial(2*n-j+1, 2*(n-j-3)).
%F A027944 a(n) = Fibonacci(2*n+9) - (8*n^6 + 12*n^5 + 110*n^4 + 465*n^3 + 1412*n^2 + 2943*n + 3060)/90.
%F A027944 G.f.: x^3*(1 + 27*x + 49*x^2 - 7*x^3 - 6*x^4)/((1-x)^7*(1-3*x+x^2)). (End)
%p A027944 with(combinat); seq(fibonacci(2*n+9) -(8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90, n=3..30); # _G. C. Greubel_, Sep 28 2019
%t A027944 Table[Fibonacci[2*n+5] -(8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90, {n,3,30}] (* _G. C. Greubel_, Sep 28 2019 *)
%o A027944 (PARI) vector(30, n, my(m=n+2); fibonacci(2*m+9) - (8*m^6 +12*m^5 +110*m^4 +465*m^3 +1412*m^2 + 2943*m +3060)/90) \\ _G. C. Greubel_, Sep 28 2019
%o A027944 (Magma) [Fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90: n in [3..30]]; // _G. C. Greubel_, Sep 28 2019
%o A027944 (Sage) [fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90 for n in (3..30)] # _G. C. Greubel_, Sep 28 2019
%o A027944 (GAP) List([3..30], n-> Fibonacci(2*n+9) - (8*n^6 +12*n^5 +110*n^4 +465*n^3 +1412*n^2 + 2943*n +3060)/90 ); # _G. C. Greubel_, Sep 28 2019
%Y A027944 Cf. A000045, A027935.
%K A027944 nonn
%O A027944 3,2
%A A027944 _Clark Kimberling_
%E A027944 Terms a(22) onward added by _G. C. Greubel_, Sep 28 2019