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 A080423 #25 Jan 11 2024 01:39:28
%S A080423 1,16,153,1134,7182,40824,214326,1058508,4979799,22517352,98513415,
%T A080423 419129802,1741000716,7083045648,28296044604,111232727064,
%U A080423 431026817373,1648861601184,6234757929477,23328137324646,86451332438394,317576323243080,1157228874847890,4185605730648420
%N A080423 a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(n+15)*3^n/360.
%H A080423 Vincenzo Librandi, <a href="/A080423/b080423.txt">Table of n, a(n) for n = 0..200</a>
%H A080423 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (18,-135,540,-1215,1458,-729).
%F A080423 G.f.: (1-2*x)/(1-3*x)^6.
%F A080423 From _G. C. Greubel_, Dec 22 2023: (Start)
%F A080423 a(n) = A136158(n+5, 5).
%F A080423 E.g.f.: (1/40)*(40 + 520*x + 1320*x^2 + 1080*x^3 + 315*x^4 + 27*x^5)*exp(3*x). (End)
%F A080423 From _Amiram Eldar_, Jan 11 2024: (Start)
%F A080423 Sum_{n>=0} 1/a(n) = 215084880*log(3/2)/1001 - 99766344351/1145144.
%F A080423 Sum_{n>=0} (-1)^n/a(n) = 216218880*log(4/3)/1001 - 498108421095/8016008. (End)
%t A080423 CoefficientList[Series[(1 - 2 x) / (1 - 3 x)^6, {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)
%t A080423 Table[3^n*(n+15)*Binomial[n+4,4]/15, {n,0,30}] (* _G. C. Greubel_, Dec 22 2023 *)
%o A080423 (Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(n+15)*3^n/360: n in [0..30]]; // _Vincenzo Librandi_, Aug 05 2013
%o A080423 (SageMath) [3^n*(n+15)*binomial(n+4,4)/15 for n in range(31)] # _G. C. Greubel_, Dec 22 2023
%Y A080423 T(n, 5) of triangle A080419.
%Y A080423 Cf. A136158.
%K A080423 easy,nonn
%O A080423 0,2
%A A080423 _Paul Barry_, Feb 19 2003