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 A139580 #25 Nov 29 2024 20:28:09
%S A139580 0,19,42,69,100,135,174,217,264,315,370,429,492,559,630,705,784,867,
%T A139580 954,1045,1140,1239,1342,1449,1560,1675,1794,1917,2044,2175,2310,2449,
%U A139580 2592,2739,2890,3045,3204,3367,3534,3705,3880,4059
%N A139580 a(n) = n*(2*n + 17).
%H A139580 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A139580 a(n) = 2*n^2 + 17*n.
%F A139580 a(n) = a(n-1) + 4*n + 15; a(0) = 0. - _Vincenzo Librandi_, Nov 24 2010
%F A139580 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A139580 G.f.: x*(19 - 15*x)/(1-x)^3.
%F A139580 E.g.f.: exp(x)*x*(19 + 2*x).
%F A139580 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A139580 a[n_]:=Sum[4*i+15, {i, 1, n}]; (* _Vladimir Joseph Stephan Orlovsky_, Dec 04 2008 *)
%t A139580 Table[n(2n+17),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,19,42},50] (* _Harvey P. Dale_, Jul 07 2024 *)
%o A139580 (PARI) a(n)=n*(2*n+17) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A139580 Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139579, A139581.
%K A139580 easy,nonn
%O A139580 0,2
%A A139580 _Omar E. Pol_, May 19 2008