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 A153785 #21 Oct 05 2024 14:38:42
%S A153785 0,5,35,90,170,275,405,560,740,945,1175,1430,1710,2015,2345,2700,3080,
%T A153785 3485,3915,4370,4850,5355,5885,6440,7020,7625,8255,8910,9590,10295,
%U A153785 11025,11780,12560,13365,14195,15050,15930,16835,17765
%N A153785 5 times heptagonal numbers: a(n) = 5*n*(5*n-3)/2.
%H A153785 G. C. Greubel, <a href="/A153785/b153785.txt">Table of n, a(n) for n = 0..1000</a>
%H A153785 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A153785 a(n) = (25*n^2 - 15*n)/2 = A000566(n)*5.
%F A153785 a(n) = 25*n + a(n-1) - 20 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F A153785 From _G. C. Greubel_, Aug 28 2016: (Start)
%F A153785 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A153785 G.f.: 5*x*(1 + 4*x)/(1 - x)^3.
%F A153785 E.g.f.: (5/2)*x*(2 + 5*x)*exp(x). (End)
%t A153785 s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,5,8!,25}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2009 *)
%t A153785 Table[5*n*(5*n - 3)/2, {n,0,25}] (* or *) LinearRecurrence[{3,-3,1}, {0,5,35}, 25] (* _G. C. Greubel_, Aug 28 2016 *)
%o A153785 (PARI) a(n) = 5*n*(5*n-3)/2; \\ _Michel Marcus_, Aug 28 2016
%Y A153785 Cf. A000566, A153784, A154786.
%K A153785 nonn,easy
%O A153785 0,2
%A A153785 _Omar E. Pol_, Jan 07 2009