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%I #13 Sep 08 2022 08:44:48
%S 1,24,379,4974,58825,651228,6891463,70602378,706070629,6931922712,
%T 67078160227,641665645062,6081300568513,57197856053076,
%U 534603948966271,4970585718586626,46011858222290077,424339730032027920
%N Expansion of 1/((1-x)(1-6x)(1-8x)(1-9x)).
%H Vincenzo Librandi, <a href="/A023954/b023954.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 (24,-197,606,-432).
%F a(n) = (35*9^(n+3) - 60*8^(n+3) + 28*6^(n+3) - 3)/840. [_Yahia Kahloune_, Jun 29 2013]
%F a(0)=1, a(1)=24, a(2)=379, a(3)=4974; for n>3, a(n) = 24*a(n-1)-197*a(n-2)+606*a(n-3)-432*a(n-4). - _Vincenzo Librandi_, Jul 16 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 8 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 16 2013 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-8*x)*(1-9*x)))); /* or */ I:=[1, 24, 379, 4974]; [n le 4 select I[n] else 24*Self(n-1)-197*Self(n-2)+606*Self(n-3)-432*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 16 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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