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 A071237 #28 Feb 08 2025 18:12:24
%S A071237 0,2,15,60,170,390,777,1400,2340,3690,5555,8052,11310,15470,20685,
%T A071237 27120,34952,44370,55575,68780,84210,102102,122705,146280,173100,
%U A071237 203450,237627,275940,318710,366270,418965,477152,541200,611490,688415,772380,863802,963110
%N A071237 a(n) = n*(n+1)*(n^2+1)/2.
%D A071237 T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
%H A071237 Vincenzo Librandi, <a href="/A071237/b071237.txt">Table of n, a(n) for n = 0..2000</a>
%H A071237 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A071237 From _Arkadiusz Wesolowski_, Apr 01 2012: (Start)
%F A071237 a(n) = A000217(n)*A002522(n).
%F A071237 a(0) = 0, a(1) = 2; for n >= 2, a(n) = ceiling(n^5/(2*n-2)) - 1.
%F A071237 G.f.: x*(2 + 5*x*(1 + x))/(1 - x)^5. (End)
%F A071237 a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5) for n>4, a(0)=0, a(1)=2, a(2)=15, a(3)=60, a(4)=170. - _Yosu Yurramendi_, Sep 03 2013
%F A071237 E.g.f.: (1/2)*x*(4 + 11*x + 7*x^2 + x^3)*exp(x). - _G. C. Greubel_, Aug 05 2024
%t A071237 Table[(n^4 + n^3 + n^2 + n)/2, {n, 0, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 07 2011 *)
%t A071237 LinearRecurrence[{5,-10,10,-5,1},{0,2,15,60,170},40] (* _Harvey P. Dale_, Feb 08 2025 *)
%o A071237 (Magma) [n*(n+1)*(n^2+1)/2: n in [0..40] ]; // _Vincenzo Librandi_, May 23 2011
%o A071237 (SageMath)
%o A071237 def A071237(n): return (n^2+1)*binomial(n+1,2)
%o A071237 [A071237(n) for n in range(51)] # _G. C. Greubel_, Aug 05 2024
%Y A071237 Cf. A027445, A037270.
%K A071237 nonn,easy
%O A071237 0,2
%A A071237 _N. J. A. Sloane_, Jun 12 2002