%I #19 Sep 08 2022 08:44:47
%S 1,27,490,7530,105991,1416477,18318520,231807060,2890036381,
%T 35658042927,436707179350,5319843165390,64552636279171,
%U 781063825879377,9430663254710980,113689073300930520,1368959098545618361
%N Expansion of 1/((1-x)(1-5x)(1-9x)(1-12x)).
%H Vincenzo Librandi, <a href="/A023772/b023772.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 (27,-239,753,-540).
%F a(n) = 27*a(n-1) - 239*a(n-2) + 753*a(n-3) - 540*a(n-4), with a(0)=1, a(1)=27, a(2)=490, a(3)=7530. [_Harvey P. Dale_, Mar 07 2012]
%F a(n) = (32*12^(n+3) - 77*9^(n+3) + 66*5^(n+3) -21)/7392. [_Yahia Kahloune_, Jun 27 2013]
%t CoefficientList[Series[1/((1-x)(1-5x)(1-9x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{27,-239,753,-540},{1,27,490,7530},30] (* _Harvey P. Dale_, Mar 07 2012 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-9*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 12 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.