%I #28 Feb 08 2024 03:11:23
%S 1,40,1005,20300,360521,5881680,90375685,1328528500,18879767841,
%T 261281940920,3540146411165,47147861315100,619093593987961,
%U 8034113714073760,103234967777291445,1315472793832108100
%N Expansion of 1/((1-8*x)*(1-9*x)*(1-11*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A016092/b016092.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 (40,-595,3900,-9504)
%F a(n) = 40*a(n-1) - 595*a(n-2) + 3900*a(n-3) - 9504*a(n-4), n>=4. - _Vincenzo Librandi_, Mar 17 2011
%F a(n) = 23*a(n-1) - 132*a(n-2) + 9^(n+1) - 8^(n+1), n>=2 . - _Vincenzo Librandi_, Mar 17 2011
%F a(n) = 12^(n+2) -2*8^(n+2)/3 - 11^(n+3)/6 + 3*9^(n+2)/2. - _R. J. Mathar_, Mar 18 2011
%t CoefficientList[Series[1/((1-8x)(1-9x)(1-11x)(1-12x)),{x,0,30}],x] (* _Harvey P. Dale_, Apr 26 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-9*x)*(1-11*x)*(1-12*x)))); // _Vincenzo Librandi_, Jun 24 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.