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 A020595 #25 Mar 26 2025 18:29:07
%S A020595 1,25,421,5965,76741,929005,10791061,121699645,1342777381,14569879885,
%T A020595 156038219701,1653799781725,17380932862021,181408804717165,
%U A020595 1882561696208341,19442349988398205,199976918230722661,2049766874087336845,20947749526851028981,213528831702049245085
%N A020595 Expansion of g.f. 1/((1-6*x)*(1-9*x)*(1-10*x)).
%H A020595 Vincenzo Librandi, <a href="/A020595/b020595.txt">Table of n, a(n) for n = 0..200</a>
%H A020595 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (25,-204,540).
%F A020595 a(0)=1, a(1)=25, a(2)=421; For n>2, a(n) = 25*a(n-1) - 204*a(n-2) + 540*a(n-3). - _Harvey P. Dale_, Oct 13 2012
%F A020595 a(n) = (3*10^(n+2) - 4*9^(n+2) + 6^(n+2))/12. - _Yahia Kahloune_, Jun 30 2013
%F A020595 a(n) = 19*a(n-1) - 90*a(n-2) + 6^n. - _Vincenzo Librandi_, Jul 04 2013
%F A020595 From _Elmo R. Oliveira_, Mar 26 2025: (Start)
%F A020595 E.g.f.: exp(6*x)*(300*exp(4*x) - 324*exp(3*x) + 36)/12.
%F A020595 a(n) = A016173(n+1) - A016172(n+1). (End)
%t A020595 CoefficientList[Series[1 / ((1 - 6 x) (1 - 9 x) (1 - 10 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{25, -204, 540}, {1, 25, 421}, 20] (* _Harvey P. Dale_, Oct 13 2012 *)
%o A020595 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-9*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 04 2013
%o A020595 (Magma) I:=[1, 25, 421]; [n le 3 select I[n] else 25*Self(n-1)-204*Self(n-2)+540*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013
%Y A020595 Cf. A016172, A016173.
%K A020595 nonn,easy
%O A020595 0,2
%A A020595 _N. J. A. Sloane_