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 A239670 #17 Jul 01 2023 14:19:20
%S A239670 1,82,6643,538084,43584805,3530369206,285959905687,23162752360648,
%T A239670 1876182941212489,151970818238211610,12309636277295140411,
%U A239670 997080538460906373292,80763523615333416236653,6541845412842006715168894,529889478440202543928680415
%N A239670 Expansion of 1/((1-x)*(1-81*x)).
%C A239670 Partial sums of 81^n.
%H A239670 Vincenzo Librandi, <a href="/A239670/b239670.txt">Table of n, a(n) for n = 0..530</a>
%H A239670 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (82, -81).
%F A239670 G.f.: 1/((1-x)*(1-81*x)).
%F A239670 a(n) = 82*a(n-1) - 81*a(n-2) for n > 1, a(0)=1, a(1)=82.
%F A239670 a(n) = 81*a(n-1) + 1 for n > 0, a(0)=1.
%F A239670 a(n) = A033119(2*n+1).
%F A239670 a(n) = ( 81^(n+1) - 1 ) / 80. [_Bruno Berselli_, Mar 24 2014]
%e A239670 Base 9................Decimal
%e A239670 1...........................1
%e A239670 101........................82
%e A239670 10101....................6643
%e A239670 1010101................538084
%e A239670 101010101............43584805
%e A239670 10101010101........3530369206
%e A239670 1010101010101....285959905687, etc.
%t A239670 CoefficientList[Series[1/((1 - x) (1 - 81 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 24 2014 *)
%o A239670 (Magma) [(81^(n+1)-1)/80: n in [0..20]]; // _Vincenzo Librandi_, Mar 24 2014
%Y A239670 Cf. A033119.
%K A239670 nonn,easy
%O A239670 0,2
%A A239670 _Philippe Deléham_, Mar 23 2014