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 A139579 #35 Nov 10 2023 09:24:02 %S A139579 0,17,38,63,92,125,162,203,248,297,350,407,468,533,602,675,752,833, %T A139579 918,1007,1100,1197,1298,1403,1512,1625,1742,1863,1988,2117,2250,2387, %U A139579 2528,2673,2822,2975,3132,3293,3458,3627,3800,3977,4158,4343,4532,4725,4922,5123,5328,5537 %N A139579 a(n) = 2*n^2 + 15*n. %H A139579 Stefano Spezia, <a href="/A139579/b139579.txt">Table of n, a(n) for n = 0..10000</a> %H A139579 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A139579 a(n) = a(n-1) + 4*n + 13; a(0) = 0. - _Vincenzo Librandi_, Nov 24 2010 %F A139579 From _Stefano Spezia_, Oct 21 2023: (Start) %F A139579 O.g.f.: x*(17 - 13*x)/(1 - x)^3. %F A139579 E.g.f.: exp(x)*x*(17 + 2*x). (End) %F A139579 From _Amiram Eldar_, Nov 10 2023: (Start) %F A139579 Sum_{n>=1} 1/a(n) = 182144/675675 - 2*log(2)/15. %F A139579 Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/15 - Pi/30 + 67952/675675. (End) %t A139579 LinearRecurrence[{3,-3,1},{0,17,38},50] (* _Stefano Spezia_, Oct 21 2023 *) %o A139579 (PARI) a(n)=2*n^2+15*n \\ _Charles R Greathouse IV_, Jun 17 2017 %Y A139579 Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139580, A139581. %K A139579 easy,nonn %O A139579 0,2 %A A139579 _Omar E. Pol_, May 19 2008