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Expansion of 1/((1-4x)(1-6x)(1-10x)).
1

%I #15 Sep 08 2022 08:44:44

%S 1,20,276,3280,36176,383040,3962176,40428800,409195776,4121666560,

%T 41395966976,415039672320,4156893515776,41607983022080,

%U 416314385842176,4164552265891840,41653977398706176,416590519605657600

%N Expansion of 1/((1-4x)(1-6x)(1-10x)).

%H Vincenzo Librandi, <a href="/A019483/b019483.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,-124,240).

%F a(n) = 4*4^n/3 -9*6^n/2 +25*10^n/6. - _R. J. Mathar_, Jun 29 2013

%F a(0)=1, a(1)=20, a(2)=276; for n>2, a(n) = 20*a(n-1) -124*a(n-2) +240*a(n-3). - _Vincenzo Librandi_, Jul 03 2013

%F a(n) = 16*a(n-1) -60*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013

%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)

%t LinearRecurrence[{20,-124,240},{1,20,276},20] (* _Harvey P. Dale_, Aug 15 2017 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-10*x)))); /* or */ I:=[1, 20, 276]; [n le 3 select I[n] else 20*Self(n-1)-124*Self(n-2)+240*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.