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 A163833 #19 Dec 17 2019 05:26:34 %S A163833 0,13,59,156,322,575,933,1414,2036,2817,3775,4928,6294,7891,9737, %T A163833 11850,14248,16949,19971,23332,27050,31143,35629,40526,45852,51625, %U A163833 57863,64584,71806,79547,87825,96658,106064,116061,126667,137900,149778 %N A163833 a(n) = n*(6*n^2 + 15*n + 5)/2. %H A163833 Vincenzo Librandi, <a href="/A163833/b163833.txt">Table of n, a(n) for n = 0..1000</a> %H A163833 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %F A163833 Row sums from A162245: a(n) = Sum_{m=1..n} (6*m*n + 3*m + 3*n + 1). %F A163833 G.f.: x*(13 + 7*x - 2*x^2)/(x-1)^4. %F A163833 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). %F A163833 E.g.f.: (1/2)*x*(26 + 33*x + 6*x^2)*exp(x). - _G. C. Greubel_, Aug 05 2017 %t A163833 CoefficientList[Series[-x*(-13-7*x+2*x^2)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 13, 59, 156}, 50](* _Vincenzo Librandi_, Mar 06 2012 *) %o A163833 (PARI) x='x+O('x^50); concat([0], Vec(x*(13 +7*x -2*x^2)/(x-1)^4)) \\ _G. C. Greubel_, Aug 05 2017 %Y A163833 Cf. A162245. %K A163833 nonn,easy %O A163833 0,2 %A A163833 _Vincenzo Librandi_, Aug 05 2009 %E A163833 Edited by _R. J. Mathar_, Aug 05 2009