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%I #13 Sep 08 2022 08:44:45
%S 1,24,388,5280,65296,760704,8515648,92705280,989122816,10397865984,
%T 108092228608,1114193633280,11410283892736,116262680100864,
%U 1179983894560768,11939165879009280,120509095367213056
%N Expansion of 1/((1-6x)(1-8x)(1-10x)).
%H Vincenzo Librandi, <a href="/A020584/b020584.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 (24,-188,480).
%F a(n) = 9*6^n/2 -16*8^n +25*10^n/2. - _R. J. Mathar_, Jun 30 2013
%F a(0)=1, a(1)=24, a(2)=388; for n>2, a(n) = 24*a(n-1) -188*a(n-2) +480*a(n-3). - _Vincenzo Librandi_, Jul 04 2013
%F a(n) = 18*a(n-1) -80*a(n-2) +6^n. - _Vincenzo Librandi_, Jul 04 2013
%t CoefficientList[Series[1 / ((1 - 6 x) (1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 04 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-8*x)*(1-10*x)))); /* or */ I:=[1,24,388]; [n le 3 select I[n] else 24*Self(n-1)-188*Self(n-2)+480*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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