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 A016191 #22 Mar 31 2025 17:21:40
%S A016191 1,21,333,4725,63261,818181,10349613,128978325,1590786621,19476859941,
%T A016191 237209103693,2877890303925,34817113183581,420347224031301,
%U A016191 5067043480830573,61010412902061525,733977975013590141,8824412881862748261,106043049217649978253,1273867442329472731125
%N A016191 Expansion of g.f. 1/((1-9*x)*(1-12*x)).
%H A016191 Harvey P. Dale, <a href="/A016191/b016191.txt">Table of n, a(n) for n = 0..900</a>
%H A016191 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (21,-108).
%F A016191 a(n) = (12^(n+1) - 9^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
%F A016191 a(n-1) = Sum_{k=1..n} 3^(n-1)*3^(n-k)*binomial(n,k). - _Zerinvary Lajos_, Sep 24 2006
%F A016191 From _Vincenzo Librandi_, Feb 09 2011: (Start)
%F A016191 a(n) = 12*a(n-1) + 9^n, a(0)=1.
%F A016191 a(n) = 21*a(n-1) - 108*a(n-2); a(0)=1, a(1)=21. (End)
%F A016191 E.g.f.: exp(9*x)*(4*exp(3*x) - 3). - _Elmo R. Oliveira_, Mar 31 2025
%t A016191 CoefficientList[Series[1/((1-9x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{21,-108},{1,21},30] (* _Harvey P. Dale_, Oct 15 2011 *)
%o A016191 (PARI) Vec(1/((1-9*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K A016191 nonn,easy
%O A016191 0,2
%A A016191 _N. J. A. Sloane_