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 A014923 #21 May 16 2025 07:19:04
%S A014923 1,19,262,3178,35983,390277,4110364,42374116,429794605,4303999495,
%T A014923 42658627906,419231343214,4090815317467,39676936914073,
%U A014923 382828823738488,3677086937252872,35178430147734169,335367700741732411,3187165771384715710,30204200124844557490,285515174765040062311
%N A014923 a(1) = 1, a(n) = n*9^(n-1) + a(n-1).
%H A014923 Vincenzo Librandi, <a href="/A014923/b014923.txt">Table of n, a(n) for n = 1..1000</a>
%H A014923 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-99,81).
%F A014923 From _Vincenzo Librandi_, Oct 23 2012: (Start)
%F A014923 a(n) = 18*a(n-1) - 81*a(n-2) + 1, a(1)=1, a(2)=19.
%F A014923 G.f.: x/((1 - x)*(1 - 9*x)^2). (End)
%F A014923 From _Elmo R. Oliveira_, May 15 2025: (Start)
%F A014923 E.g.f.: exp(x)*(1 + exp(8*x)*(72*x - 1))/64.
%F A014923 a(n) = (9^n*(8*n - 1) + 1)/64.
%F A014923 a(n) = 19*a(n-1) - 99*a(n-2) + 81*a(n-3) for n >= 4. (End)
%t A014923 CoefficientList[Series[1/((1 - x)(1 - 9*x)^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 23 2012 *)
%o A014923 (Magma) I:=[1, 19]; [n le 2 select I[n] else 18*Self(n-1) - 81*Self(n-2) + 1: n in [1..30]]; // _Vincenzo Librandi_, Oct 23 2012
%o A014923 (PARI) Vec(x/((1 - x)*(1 - 9*x)^2) + O(x^30)) \\ _Jinyuan Wang_, Mar 11 2020
%K A014923 nonn,easy
%O A014923 1,2
%A A014923 _Olivier Gérard_