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 A027658 #22 Feb 27 2023 13:37:03
%S A027658 1,4,12,31,71,147,280,498,837,1342,2068,3081,4459,6293,8688,11764,
%T A027658 15657,20520,26524,33859,42735,53383,66056,81030,98605,119106,142884,
%U A027658 170317,201811,237801,278752,325160,377553,436492,502572,576423,658711,750139,851448
%N A027658 a(n) = binomial(n+2, 2) + binomial(n+4, 5).
%H A027658 Vincenzo Librandi, <a href="/A027658/b027658.txt">Table of n, a(n) for n = 0..1000</a>
%H A027658 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A027658 G.f.: (1 - 2*x + 3*x^2 - x^3)/(1-x)^6. - _Colin Barker_, Apr 15 2013
%F A027658 From _R. J. Mathar_, Sep 29 2020: (Start)
%F A027658 a(n) = A000217(n+1) + A000389(n+4)
%F A027658 a(n) = (n+1)*(n+2)*(60 +12*n +7*n^2 +n^3)/120. (End)
%F A027658 From _G. C. Greubel_, Aug 01 2022: (Start)
%F A027658 a(n) = Sum_{j=1..2} binomial(n+2*j, 3*j-1).
%F A027658 E.g.f.: (1/120)*(120 + 360*x + 300*x^2 + 120*x^3 + 20*x^4 + x^5)*exp(x). (End)
%t A027658 CoefficientList[Series[(1-2*x+3*x^2-x^3)/(1-x)^6, {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 18 2013 *)
%t A027658 Sum[Binomial[2*j +Range[0, 60], 3*j-1], {j,2}] (* _G. C. Greubel_, Aug 01 2022 *)
%t A027658 LinearRecurrence[{6,-15,20,-15,6,-1},{1,4,12,31,71,147},40] (* _Harvey P. Dale_, Feb 27 2023 *)
%o A027658 (Magma) [(60 +12*n +7*n^2 +n^3)*Binomial(n+2,2)/60: n in [0..60]]; // _G. C. Greubel_, Aug 01 2022
%o A027658 (SageMath) [(60 +12*n +7*n^2 +n^3)*binomial(n+2,2)/60 for n in (0..60)] # _G. C. Greubel_, Aug 01 2022
%Y A027658 Cf. A000217, A000389.
%K A027658 nonn,easy
%O A027658 0,2
%A A027658 _N. J. A. Sloane_