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 A162261 #31 Jan 21 2025 03:25:22
%S A162261 0,11,39,90,170,285,441,644,900,1215,1595,2046,2574,3185,3885,4680,
%T A162261 5576,6579,7695,8930,10290,11781,13409,15180,17100,19175,21411,23814,
%U A162261 26390,29145,32085,35216,38544,42075,45815,49770,53946,58349,62985,67860
%N A162261 a(n) = (2*n^3 + 5*n^2 - 7*n)/2.
%H A162261 Vincenzo Librandi, <a href="/A162261/b162261.txt">Table of n, a(n) for n = 1..1000</a>
%H A162261 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A162261 Row sums from A155724: a(n) = Sum_{m=1..n} (2*m*n + m + n - 4).
%F A162261 From _Vincenzo Librandi_, Mar 04 2012: (Start)
%F A162261 G.f.: x^2*(11 - 5*x)/(1-x)^4.
%F A162261 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%F A162261 a(n) = A151675(n) - 8*n. - _L. Edson Jeffery_, Oct 12 2012
%F A162261 From _Amiram Eldar_, Feb 25 2023: (Start)
%F A162261 Sum_{n>=2} 1/a(n) = 8*log(2)/63 + 1166/19845.
%F A162261 Sum_{n>=2} (-1)^n/a(n) = (32*log(2) - 2*Pi - 3566/315)/63. (End)
%F A162261 E.g.f.: (1/2)*x^2*(11 + 2*x)*exp(x). - _G. C. Greubel_, Jan 21 2025
%t A162261 CoefficientList[Series[x*(11-5*x)/(1-x)^4,{x,0,40}],x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 11, 39, 90}, 50](* _Vincenzo Librandi_, Mar 04 2012 *)
%o A162261 (Magma) [(2*n^3 + 5*n^2 - 7*n)/2 : n in [1..50]]; // _Wesley Ivan Hurt_, May 07 2021
%o A162261 (Python)
%o A162261 def A162261(n): return n*(2*pow(n,2) +5*n -7)//2
%o A162261 print([A162261(n) for n in range(1,61)]) # _G. C. Greubel_, Jan 21 2025
%Y A162261 Cf. A151675, A155724.
%K A162261 nonn,easy
%O A162261 1,2
%A A162261 _Vincenzo Librandi_, Jun 29 2009
%E A162261 New name from _Vincenzo Librandi_, Mar 04 2012