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 A133252 #14 Apr 21 2024 22:04:00
%S A133252 1,5,17,45,100,196,350,582,915,1375,1991,2795,3822,5110,6700,8636,
%T A133252 10965,13737,17005,20825,25256,30360,36202,42850,50375,58851,68355,
%U A133252 78967,90770,103850,118296,134200,151657,170765,191625,214341,239020,265772
%N A133252 Partial sums of A006000.
%C A133252 Prime for a(1) = 5, a(2) = 17, then never again?
%H A133252 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A133252 a(n) = Sum_{i=0..n} A006000(i).
%F A133252 a(n) = Sum_{i=0..n} (i+1)*(i^2+i+2)/2.
%F A133252 a(n) = ((n^4+2*n^3+n^2)/4+(2*n^3+3*n^2+n)/3+(3*n^2+3*n)/2+2*n)/2+1.
%F A133252 G.f.: -(2*x^2 + 1) / (x-1)^5. - _Colin Barker_, Apr 28 2013
%F A133252 a(n) = (n+1)*(n+2)*(3*n^2+5*n+12)/24. - _Alois P. Heinz_, Apr 28 2013
%F A133252 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Wesley Ivan Hurt_, Apr 21 2024
%t A133252 LinearRecurrence[{5,-10,10,-5,1},{1,5,17,45,100},40] (* _Harvey P. Dale_, Sep 15 2022 *)
%Y A133252 Cf. A006000.
%K A133252 easy,nonn
%O A133252 0,2
%A A133252 _Jonathan Vos Post_, Dec 19 2007