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%I #19 Sep 08 2022 08:44:45
%S 1,17,194,1882,16827,143835,1197868,9822164,79783253,644325253,
%T 5184986742,41632083246,333818409679,2674358387471,21413929824416,
%U 171406773741928,1371730930238505,10976231337133689,87821770754328490
%N Expansion of 1/((1-x)(1-3x)(1-5x)(1-8x)).
%H Vincenzo Librandi, <a href="/A021434/b021434.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (17,-95,199,-120).
%F a(n) = (8^(n+4) - 7*5^(n+4) + 14*3^(n+4) - 15)/840. - _Yahia Kahloune_, Jul 05 2013
%F a(0)=1, a(1)=17; for n>1, a(n) = 13*a(n-1) -40*a(n-2) +(3^n-1)/2. - _Vincenzo Librandi_, Jul 10 2013
%F a(0)=1, a(1)=17, a(2)=194, a(3)=1882; for n>3, a(n) = 17*a(n-1) -95*a(n-2) +199*a(n-3) -120*a(n-4). - _Vincenzo Librandi_, Jul 10 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 5 x) (1 - 8 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 10 2013 *)
%t LinearRecurrence[{17,-95,199,-120},{1,17,194,1882},20] (* _Harvey P. Dale_, Dec 10 2017 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-8*x)))); /+ or */ I:=[1, 17, 194, 1882]; [n le 4 select I[n] else 17*Self(n-1)-95*Self(n-2)+199*Self(n-3)-120*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 10 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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