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 A116166 #33 Mar 10 2025 13:57:06
%S A116166 0,16,384,6144,81920,983040,11010048,117440512,1207959552,12079595520,
%T A116166 118111600640,1133871366144,10720238370816,100055558127616,
%U A116166 923589767331840,8444249301319680,76561193665298432,689050742987685888
%N A116166 a(n) = 8^n * n*(n+1).
%H A116166 Vincenzo Librandi, <a href="/A116166/b116166.txt">Table of n, a(n) for n = 0..1000</a>
%H A116166 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (24,-192,512).
%F A116166 G.f.: 16*x/(1-8*x)^3. - _Vincenzo Librandi_, Feb 28 2013
%F A116166 a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3). - _Vincenzo Librandi_, Feb 28 2013
%F A116166 a(n) = 16*A081138(n+1). - _Bruno Berselli_, Feb 28 2013
%F A116166 E.g.f.: 16*x*(1 + 4*x)*exp(8*x). - _G. C. Greubel_, May 11 2019
%F A116166 From _Amiram Eldar_, Jul 20 2020: (Start)
%F A116166 Sum_{n>=1} 1/a(n) = 1 - 7*log(8/7).
%F A116166 Sum_{n>=1} (-1)^(n+1)/a(n) = 9*log(9/8) - 1. (End)
%t A116166 Table[(n^2 + n) 8^n, {n, 0, 30}] (* _Harvey P. Dale_, Mar 09 2011 *)
%t A116166 CoefficientList[Series[16 x/(1 - 8 x)^3, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 28 2013 *)
%o A116166 (Magma) [(n^2+n)*8^n: n in [0..30]]; // _Vincenzo Librandi_, Feb 28 2013
%o A116166 (PARI) a(n)=(n^2+n)*8^n \\ _Charles R Greathouse IV_, Feb 28 2013
%o A116166 (Sage) [8^n*n*(n+1) for n in (0..30)] # _G. C. Greubel_, May 11 2019
%o A116166 (GAP) List([0..30], n-> 8^n*n*(n+1)); # _G. C. Greubel_, May 11 2019
%Y A116166 Cf. A007758, A036289, A081138, A128796.
%K A116166 nonn,easy
%O A116166 0,2
%A A116166 _Mohammad K. Azarian_, Apr 08 2007