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 A128800 #24 Apr 04 2025 03:27:13
%S A128800 0,0,72,1296,15552,155520,1399680,11757312,94058496,725594112,
%T A128800 5441955840,39907676160,287335268352,2037468266496,14262277865472,
%U A128800 98738846760960,677066377789440,4604051368968192,31077346740535296,208401031083589632,1389340207223930880,9213519268958699520
%N A128800 a(n) = n*(n-1)*6^n.
%H A128800 Vincenzo Librandi, <a href="/A128800/b128800.txt">Table of n, a(n) for n = 0..1000</a>
%H A128800 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-108,216).
%F A128800 G.f.: 72*x^2/(1 - 6*x)^3. - _Vincenzo Librandi_, Feb 11 2013
%F A128800 a(n) = 72*A081136(n). - _R. J. Mathar_, Apr 26 2015
%F A128800 a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3). - _Wesley Ivan Hurt_, Jan 20 2024
%F A128800 From _Amiram Eldar_, Apr 04 2025: (Start)
%F A128800 Sum_{n>=2} 1/a(n) = 1/6 - (5/6)*log(6/5).
%F A128800 Sum_{n>=2} (-1)^n/a(n) = (7/6)*log(7/6) - 1/6. (End)
%t A128800 CoefficientList[Series[72 x^2/(1 - 6 x)^3, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 11 2013 *)
%t A128800 LinearRecurrence[{18,-108,216},{0,0,72},30] (* _Harvey P. Dale_, Mar 22 2018 *)
%o A128800 (Magma) [(n^2-n)*6^n: n in [0..25]]; // _Vincenzo Librandi_, Feb 11 2013
%Y A128800 Cf. A007758, A036289, A081136.
%K A128800 nonn,easy
%O A128800 0,3
%A A128800 _Mohammad K. Azarian_, Apr 07 2007