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 A128803 #32 Jun 26 2025 07:58:49
%S A128803 0,0,162,4374,78732,1180980,15943230,200884698,2410616376,27894275208,
%T A128803 313810596090,3451916556990,37280698815492,396531069219324,
%U A128803 4163576226802902,43237137739876290,444724845324441840
%N A128803 a(n) = n*(n-1)*9^n.
%H A128803 Vincenzo Librandi, <a href="/A128803/b128803.txt">Table of n, a(n) for n = 0..1000</a>
%H A128803 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (27,-243,729).
%F A128803 From _Vincenzo Librandi_, Feb 12 2013: (Start)
%F A128803 G.f.: 162*x^2/(1-9*x)^3.
%F A128803 a(n) = 27*a(n-1)-243*a(n-2)+729*a(n-3). (End)
%F A128803 a(n) = 162*A081139(n). - _R. J. Mathar_, Apr 26 2015
%F A128803 From _Amiram Eldar_, Jun 26 2025: (Start)
%F A128803 Sum_{n>=2} 1/a(n) = 1/9 - (8/9)*log(9/8).
%F A128803 Sum_{n>=2} (-1)^n/a(n) = (10/9)*log(10/9) - 1/9. (End)
%t A128803 LinearRecurrence[{27, -243, 729}, {0, 0, 162}, 30] (* or *) CoefficientList[Series[162 x^2/(1 - 9 x)^3, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 12 2013 *)
%o A128803 (Magma) [(n^2-n)*9^n: n in [0..25]]; // _Vincenzo Librandi_, Feb 12 2013
%o A128803 (Magma) I:=[0,0,162]; [n le 3 select I[n] else 27*Self(n-1)-243*Self(n-2)+729*Self(n-3): n in [1..25]]; // _Vincenzo Librandi_, Feb 12 2013
%Y A128803 Cf. A036289, A007758, A081139.
%K A128803 nonn,easy
%O A128803 0,3
%A A128803 _Mohammad K. Azarian_, Apr 07 2007