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 A085786 #33 May 08 2022 10:08:55
%S A085786 2,11,33,74,140,237,371,548,774,1055,1397,1806,2288,2849,3495,4232,
%T A085786 5066,6003,7049,8210,9492,10901,12443,14124,15950,17927,20061,22358,
%U A085786 24824,27465,30287,33296,36498,39899,43505,47322,51356,55613,60099,64820
%N A085786 a(n) = n*(2*n^2 + n + 1)/2.
%H A085786 Vincenzo Librandi, <a href="/A085786/b085786.txt">Table of n, a(n) for n = 1..1000</a>
%H A085786 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A085786 a(n) = A000217(n) + n^3.
%F A085786 From _Colin Barker_, Jan 20 2014: (Start)
%F A085786 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A085786 G.f.: x*(x+1)*(x+2) / (x-1)^4. (End)
%F A085786 E.g.f.: (x/2)*(4 + 7*x + 2*x^2)*exp(x). - _G. C. Greubel_, Aug 24 2017
%t A085786 CoefficientList[Series[(x + 1) (x + 2) / (x - 1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 11, 33, 74}, 40] (* _Vincenzo Librandi_, Aug 14 2017 *)
%o A085786 (PARI) t(n)=n*(n+1)/2;
%o A085786 vector(40, i, t(i)+i^3)
%o A085786 (Magma) [n*(2*n^2 + n + 1)/2: n in [1..40]]; // _Vincenzo Librandi_, Aug 14 2017
%Y A085786 Cf. A000217 [t(n)], A000096 [t(n)+n], A005449 [t(n)+n^2].
%Y A085786 a(n) = A110449(n, n).
%K A085786 nonn,easy
%O A085786 1,1
%A A085786 _Jon Perry_, Jul 23 2003
%E A085786 Name changed by _Wesley Ivan Hurt_, Apr 30 2022