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 A021714 #17 Jul 08 2025 08:50:01
%S A021714 1,25,428,6278,84879,1092243,13601506,165488176,1979095877,
%T A021714 23357343581,272803757304,3159571375194,36342586372795,
%U A021714 415641464948839,4730786270092622,53625950549096132,605758471885400433
%N A021714 Expansion of 1/((1-x)(1-3x)(1-10x)(1-11x)).
%H A021714 Vincenzo Librandi, <a href="/A021714/b021714.txt">Table of n, a(n) for n = 0..200</a>
%H A021714 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (25,-197,503,-330).
%F A021714 G.f.: 1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x)).
%F A021714 a(n) = -1/180 +3^(n+3)/112 -10^(n+3)/63 +11^(n+3)/80. [_Bruno Berselli_, May 07 2013]
%F A021714 a(n)-11*a(n-1) = A016215(n). [_Bruno Berselli_, May 08 2013]
%t A021714 CoefficientList[Series[1/((1 - x) (1 - 3 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* _Bruno Berselli_, May 07 2013 *)
%t A021714 LinearRecurrence[{25,-197,503,-330},{1,25,428,6278},20] (* _Harvey P. Dale_, Jan 16 2024 *)
%o A021714 (PARI) Vec(1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x))+O(x^20)) \\ _Bruno Berselli_, May 07 2013
%o A021714 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-10*x)*(1-11*x)))); // _Bruno Berselli_, May 07 2013
%Y A021714 Cf. A016215, A018206 (first differences).
%K A021714 nonn,easy
%O A021714 0,2
%A A021714 _N. J. A. Sloane_