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 A116164 #27 Nov 18 2024 12:05:02
%S A116164 0,12,216,2592,25920,233280,1959552,15676416,120932352,906992640,
%T A116164 6651279360,47889211392,339578044416,2377046310912,16456474460160,
%U A116164 112844396298240,767341894828032,5179557790089216,34733505180598272
%N A116164 a(n) = 6^n * n*(n+1).
%H A116164 Vincenzo Librandi, <a href="/A116164/b116164.txt">Table of n, a(n) for n = 0..1000</a>
%H A116164 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-108,216).
%F A116164 G.f.: 12*x/(1-6*x)^3. - _Vincenzo Librandi_, Feb 28 2013
%F A116164 a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3). - _Vincenzo Librandi_, Feb 28 2013
%F A116164 a(n) = 12*A081136(n+1). - _Bruno Berselli_, Feb 28 2013
%F A116164 E.g.f.: 12*x*(1 + 3*x)*exp(6*x). - _G. C. Greubel_, May 10 2019
%F A116164 From _Amiram Eldar_, Jul 20 2020: (Start)
%F A116164 Sum_{n>=1} 1/a(n) = 1 - 5*log(6/5).
%F A116164 Sum_{n>=1} (-1)^(n+1)/a(n) = 7*log(7/6) - 1. (End)
%t A116164 Table[(n^2 + n) 6^n, {n, 0, 30}] (* or *) CoefficientList[Series[12 x/(1 - 6 x)^3, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 28 2013 *)
%o A116164 (Magma) [(n^2+n)*6^n: n in [0..30]]; // _Vincenzo Librandi_, Feb 28 2013
%o A116164 (Magma) I:=[0,12,216]; [n le 3 select I[n] else 18*Self(n-1)-108*Self(n-2)+216*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Feb 28 2013
%o A116164 (PARI) a(n)=(n^2+n)*6^n \\ _Charles R Greathouse IV_, Feb 28 2013
%o A116164 (Sage) [6^n*n*(n+1) for n in (0..30)] # _G. C. Greubel_, May 10 2019
%o A116164 (GAP) List([0..30], n-> 6^n*n*(n+1) ); # _G. C. Greubel_, May 10 2019
%Y A116164 Cf. A007758, A036289, A081136, A128796.
%K A116164 nonn,easy
%O A116164 0,2
%A A116164 _Mohammad K. Azarian_, Apr 08 2007