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 A174121 #9 Sep 23 2019 16:52:24
%S A174121 1,4,12,29,61,118,218,395,715,1308,2432,4601,8841,17202,33782,66775,
%T A174121 132567,263928,526396,1051045,2100021,4197614,8392402,16781539,
%U A174121 33559331,67114388,134223928,268442385,536878625,1073750378,2147493102,4294977711,8589946031
%N A174121 Partial sums of A001580.
%C A174121 A001580 2^n+n^2 -> 1,3,8,17,32,57,100,177,320,593,1124,..
%H A174121 Colin Barker, <a href="/A174121/b174121.txt">Table of n, a(n) for n = 1..1000</a>
%H A174121 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).
%F A174121 From _Colin Barker_, Feb 26 2016: (Start)
%F A174121 a(n) = (n-2)*(2*n^2+n+3)/6+2^n.
%F A174121 a(n) = 6*a(n-1)-14*a(n-2)+16*a(n-3)-9*a(n-4)+2*a(n-5) for n>5.
%F A174121 G.f.: x*(1-2*x+2*x^2-3*x^3) / ((1-x)^4*(1-2*x)).
%F A174121 (End)
%t A174121 f[n_]:=Sum[2^i+i^2,{i,0,n}];Table[f[n],{n,0,5!}]
%t A174121 Accumulate[Table[2^n+n^2,{n,0,50}]] (* or *) LinearRecurrence[{6,-14,16,-9,2},{1,4,12,29,61},50] (* _Harvey P. Dale_, Sep 23 2019 *)
%o A174121 (PARI) Vec(x*(1-2*x+2*x^2-3*x^3)/((1-x)^4*(1-2*x)) + O(x^40)) \\ _Colin Barker_, Feb 26 2016
%Y A174121 Cf. A174120.
%K A174121 nonn,easy
%O A174121 1,2
%A A174121 _Vladimir Joseph Stephan Orlovsky_, Mar 08 2010