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%I #16 Sep 08 2022 08:44:45
%S 1,20,263,2878,28449,264048,2350651,20332466,172311557,1438844836,
%T 11885079999,97387603014,793247778025,6432389826584,51985193621507,
%U 419076145997722,3371967484999053,27092843456412492
%N Expansion of 1/((1-x)(1-5x)(1-6x)(1-8x)).
%H Vincenzo Librandi, <a href="/A022111/b022111.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (20,-137,358,-240)
%F a(n) = 256*8^n/21 -108*6^n/5 + 125*5^n/12 -1/140. - _R. J. Mathar_, Mar 11 2011
%F a(0)=1, a(1)=20, a(2)=263, a(3)=2878, a(n)=20*a(n-1)-137*a(n-2)+ 358*a(n-3)- 240*a(n-4). - _Harvey P. Dale_, Nov 04 2012
%t CoefficientList[Series[1/((1-x)(1-5x)(1-6x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{20,-137,358,-240},{1,20,263,2878},30] (* _Harvey P. Dale_, Nov 04 2012 *)
%o (Magma) I:=[1, 20, 263, 2878]; [n le 4 select I[n] else 20*Self(n-1)-137*Self(n-2)+358*Self(n-3)-240*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-6*x)*(1-8*x)))); // _Vincenzo Librandi_, Jul 12 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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