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%I #18 Sep 08 2022 08:44:48
%S 1,27,487,7407,102943,1357119,17315839,216369279,2667080575,
%T 32582253951,395677903231,4786097041791,57739474264447,
%U 695339842109823,8363901349806463,100525966375567743,1207588183261823359
%N Expansion of 1/((1-x)(1-6x)(1-8x)(1-12x)).
%H Vincenzo Librandi, <a href="/A024114/b024114.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (27,-242,792,-576).
%F a(n) = (35*12^(n+3) - 165*8^(n+3) + 154*6^(n+3) - 24)/9240. [_Yahia Kahloune_, Jun 27 2013]
%F a(0)=1, a(1)=27, a(2)=487, a(3)=7407; for n>3, a(n) = 27*a(n-1) -242*a(n-2) +792*a(n-3) -576*a(n-4). - _Vincenzo Librandi_, Jul 16 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 16 2013 *)
%t LinearRecurrence[{27,-242,792,-576},{1,27,487,7407},20] (* _Harvey P. Dale_, Jan 25 2019 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-8*x)*(1-12*x)))); /* or */ I:=[1,27,487,7407]; [n le 4 select I[n] else 27*Self(n-1)-242*Self(n-2)+792*Self(n-3)-576*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 16 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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