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 A021814 #14 Jul 08 2025 08:57:51
%S A021814 1,19,239,2519,24135,218343,1903783,16194343,135426599,1118993447,
%T A021814 9166829607,74629521447,604827848743,4885462331431,39365093814311,
%U A021814 316610553147431,2543028967600167,20405121901817895
%N A021814 Expansion of 1/((1-x)(1-4x)(1-6x)(1-8x)).
%H A021814 Vincenzo Librandi, <a href="/A021814/b021814.txt">Table of n, a(n) for n = 0..200</a>
%H A021814 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (19,-122,296,-192).
%F A021814 G.f.: 1/((1-x)*(1-4*x)*(1-6*x)*(1-8*x)).
%F A021814 a(n) = -1/105 +2^(2n+3)/3 -2^(n+1)*3^(n+3)/5 +8^(n+2)/7. [_Bruno Berselli_, May 08 2013]
%t A021814 CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* _Bruno Berselli_, May 08 2013 *)
%o A021814 (PARI) Vec(1/((1-x)*(1-4*x)*(1-6*x)*(1-8*x))+O(x^20)) \\ _Bruno Berselli_, May 08 2013
%o A021814 (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-6*x)*(1-8*x)))); // _Bruno Berselli_, May 08 2013
%Y A021814 Cf. A019333 (first differences).
%K A021814 nonn,easy
%O A021814 0,2
%A A021814 _N. J. A. Sloane_