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 A014903 #33 Mar 31 2025 15:37:50
%S A014903 1,21,402,7642,145203,2758863,52418404,995949684,18923044005,
%T A014903 359537836105,6831218886006,129793158834126,2466070017848407,
%U A014903 46855330339119747,890251276443275208,16914774252422228968,321380710796022350409,6106233505124424657789,116018436597364068498010
%N A014903 a(1)=1, a(n) = 19*a(n-1) + n.
%H A014903 Vincenzo Librandi, <a href="/A014903/b014903.txt">Table of n, a(n) for n = 1..200</a>
%H A014903 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-39,19).
%F A014903 a(1)=1, a(2)=21, a(3)=402, a(n) = 21*a(n-1) - 39*a(n-2) + 19*a(n-3). - _Vincenzo Librandi_, Oct 20 2012
%F A014903 From _Elmo R. Oliveira_, Mar 29 2025: (Start)
%F A014903 G.f.: x/((1-19*x)*(1-x)^2).
%F A014903 E.g.f.: exp(x)*(19*exp(18*x) - 18*x - 19)/324.
%F A014903 a(n) = (19^(n+1) - 18*n - 19)/324. (End)
%t A014903 LinearRecurrence[{21, -39, 19}, {1, 21, 402}, 20] (* _Vincenzo Librandi_, Oct 20 2012 *)
%o A014903 (Magma) I:=[1, 21, 402]; [n le 3 select I[n] else 21*Self(n-1) - 39*Self(n-2) + 19*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2012
%Y A014903 Row n=19 of A126885.
%K A014903 nonn,easy
%O A014903 1,2
%A A014903 _N. J. A. Sloane_, _Olivier Gérard_