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%I #20 Sep 08 2022 08:44:45
%S 1,30,604,10200,156016,2241120,30844864,411749760,5373888256,
%T 68949788160,873102490624,10942870149120,136039563882496,
%U 1680275743334400,20645716733968384,252607863319265280
%N Expansion of 1/((1-8*x)*(1-10*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A020980/b020980.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (30,-296,960).
%F a(n) = (12^(n+2) - 2*10^(n+2) + 8^(n+2))/8. - _Yahia Kahloune_, Jun 30 2013
%F a(0)=1, a(1)=30, a(2)=604; for n>2, a(n) = 30*a(n-1) -296*a(n-2) +960*a(n-3). - _Vincenzo Librandi_, Jul 05 2013
%F a(n) = 22*a(n-1) -120*a(n-2) +8^n. - _Vincenzo Librandi_, Jul 05 2013
%t CoefficientList[Series[1 / ((1 - 8 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* _Harvey P. Dale_, Mar 23 2011 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-10*x)*(1-12*x)))); /* or */ I:=[1, 30, 604]; [n le 3 select I[n] else 30*Self(n-1)-296*Self(n-2)+960*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 05 2013
%o (PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-10*x)*(1-12*x))) \\ _G. C. Greubel_, Feb 09 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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