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 A014940 #23 May 21 2025 01:35:25
%S A014940 1,45,1497,44089,1215369,32137161,825796489,20780659593,514663521417,
%T A014940 12587355699337,304746506405001,7316566123340937,174431600326980745,
%U A014940 4133772410690139273,97461091512107447433,2287542179758700278921,53480687617522807714953,1245979840167792604460169
%N A014940 a(1)=1, a(n) = n*22^(n-1) + a(n-1).
%H A014940 Vincenzo Librandi, <a href="/A014940/b014940.txt">Table of n, a(n) for n = 1..200</a>
%H A014940 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (45,-528,484).
%F A014940 G.f.: x/((1-x)*(-1+22*x)^2). - _Harvey P. Dale_, Apr 21 2011
%F A014940 From _Elmo R. Oliveira_, May 18 2025: (Start)
%F A014940 E.g.f.: exp(x)*(1 + exp(21*x)*(462*x - 1))/441.
%F A014940 a(n) = (22^n*(21*n - 1) + 1)/441.
%F A014940 a(n) = 44*a(n-1) - 484*a(n-2) + 1 for n > 2.
%F A014940 a(n) = 45*a(n-1) - 528*a(n-2) + 484*a(n-3) for n > 3. (End)
%t A014940 Table[(1+22^n (21n-1))/441,{n,20}] (* or *) CoefficientList[ Series[1/((1-x) (-1+22 x)^2),{x,0,20}],x] (* _Harvey P. Dale_, Apr 21 2011 *)
%K A014940 nonn,easy
%O A014940 1,2
%A A014940 _Olivier Gérard_