%I #14 Sep 08 2022 08:44:48

%S 1,28,527,8390,122121,1683768,22407907,291019450,3713967341,

%T 46787388908,583658682087,7226065372110,88934701511761,

%U 1089437114484448,13295459966641067,161767703674942370

%N Expansion of 1/((1-x)(1-5x)(1-10x)(1-12x)).

%H Vincenzo Librandi, <a href="/A023947/b023947.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 (28,-257,830,-600).

%F a(n) = (90*12^(n+3) - 154*10^(n+3) + 99*5^(n+3) - 35)/13860. [_Yahia Kahloune_, Jun 27 2013]

%F a(0)=1, a(1)=28, a(2)=527, a(3)=8390; for n>3, a(n) = 28*a(n-1) -257*a(n-2) +830*a(n-3) -600*a(n-4). - _Vincenzo Librandi_, Jul 12 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)

%o (Magma) I:=[1,28,527,8390]; [n le 4 select I[n] else 28*Self(n-1)-257*Self(n-2)+830*Self(n-3)-600*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-10*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 12 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.