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 A027007 #16 Jul 25 2025 15:32:20
%S A027007 1,53,634,4201,20120,78753,269829,844702,2486178,7017354,19260116,
%T A027007 51903794,138254821,365619439,962704734,2528441803,6631057180,
%U A027007 17376467099,45514392201,119188310928,312079208726,817086876180,2139230058328,5600665608772,14662845807193
%N A027007 a(n) = A026998(2n+1, n+4).
%H A027007 G. C. Greubel, <a href="/A027007/b027007.txt">Table of n, a(n) for n = 3..1000</a>
%H A027007 <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 A027007 From _G. C. Greubel_, Jul 23 2025: (Start)
%F A027007 a(n) = Lucas(2*n+9) - (1/30)*(8*n^6 - 4*n^5 + 110*n^4 + 325*n^3 + 1052*n^2 + 2199*n + 2280).
%F A027007 G.f.: x^3*(1 + 43*x + 147*x^2 + 35*x^3 - 32*x^4 - 2*x^5)/((1-x)^7*(1-3*x+x^2)).
%F A027007 E.g.f.: 4*exp(3*x/2)*( 19*cosh(p*x) + 17*p*sinh(p*x) ) - (1/30)*(2280 + 3690*x + 2985*x^2 + 1605*x^3 + 590*x^4 + 116*x^5 + 8*x^6)*exp(x), where 2*p = sqrt(5). (End)
%t A027007 Table[LucasL[2*n+9] -(1/30)*(8*n^6 -4*n^5 +110*n^4 +325*n^3 +1052*n^2 +2199*n +2280), {n,3,45}] (* _G. C. Greubel_, Jul 23 2025 *)
%o A027007 (Magma)
%o A027007 A027007:= func< n | Lucas(2*n+9) - (1/30)*(8*n^6 - 4*n^5 + 110*n^4 + 325*n^3 + 1052*n^2 + 2199*n + 2280) >;
%o A027007 [A027007(n): n in [3..45]]; // _G. C. Greubel_, Jul 23 2025
%o A027007 (SageMath)
%o A027007 def A027007(n): return lucas_number2(2*n+9,1,-1) - (1/30)*(8*n^6 - 4*n^5 + 110*n^4 + 325*n^3 + 1052*n^2 + 2199*n + 2280)
%o A027007 print([A027007(n) for n in range(3,46)]) # _G. C. Greubel_, Jul 23 2025
%Y A027007 Cf. A000032, A026998.
%K A027007 nonn,easy
%O A027007 3,2
%A A027007 _Clark Kimberling_
%E A027007 More terms from _Sean A. Irvine_, Oct 21 2019