%I #13 Sep 08 2022 08:44:45
%S 1,20,285,3640,44681,540540,6505045,78138080,937976961,11257033060,
%T 135089723405,1621098253320,19453266126841,233439544261580,
%U 2801275941271365,33615316957309360,403383826200494321
%N Expansion of 1/((1-x)(1-3x)(1-4x)(1-12x)).
%H Vincenzo Librandi, <a href="/A021404/b021404.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,-115,240,-144).
%F a(0)=1, a(1)=20, a(2)=285, a(3)=3640, a(n) = 20*a(n-1)-115*a(n-2)+240*a(n-3)- 144*a(n-4). [_Harvey P. Dale_, May 06 2012]
%F a(0)=1, a(1)=20; for n>1, a(n) = 16*a(n-1) -48*a(n-2) +(3^n-1)/2. - _Vincenzo Librandi_, Jul 09 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 12 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{20, -115, 240, -144}, {1, 20, 285, 3640}, 30] (* _Harvey P. Dale_, May 06 2012 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-12*x)))); /* or */ I:=[1, 20, 285, 3640]; [n le 4 select I[n] else 20*Self(n-1)-115*Self(n-2)+240*Self(n-3)-144*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 09 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.