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 A019443 #18 Jan 22 2025 14:13:26
%S A019443 1,19,247,2743,28063,273847,2596399,24174631,222479455,2032023895,
%T A019443 18467516431,167287650439,1512085646527,13647818683063,
%U A019443 123064923768943,1108992721390567,9989389232302879,89955248709321751
%N A019443 Expansion of 1/((1-4x)(1-6x)(1-9x)).
%H A019443 Vincenzo Librandi, <a href="/A019443/b019443.txt">Table of n, a(n) for n = 0..200</a>
%H A019443 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (19,-114,216).
%F A019443 a(n) = 8*4^n/5 -6*6^n +27*9^n/5. - _R. J. Mathar_, Jun 29 2013
%F A019443 a(0)=1, a(1)=19, a(2)=247; for n>2, a(n) = 19*a(n-1) -114*a(n-2) +216*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F A019443 a(n) = 15*a(n-1) -54*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013
%t A019443 CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 9 x)),{x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t A019443 LinearRecurrence[{19,-114,216},{1,19,247},30] (* _Harvey P. Dale_, Oct 04 2019 *)
%o A019443 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-9*x)))); // _Vincenzo Librandi_, Jul 03 2013
%o A019443 (Magma) I:=[1, 19, 247]; [n le 3 select I[n] else 19*Self(n-1)-114*Self(n-2)+216*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K A019443 nonn,easy
%O A019443 0,2
%A A019443 _N. J. A. Sloane_