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%I #12 Jun 03 2023 11:09:25
%S 1,40,1007,20414,364329,5979036,92485219,1369339018,19606630637,
%T 273438929192,3733694351751,50109751007862,662977655746225,
%U 8667106208101108,112162143040653803,1438993526155501346
%N Expansion of 1/((1-7x)(1-10x)(1-11x)(1-12x)).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (40, -593, 3854, -9240).
%F From _Vincenzo Librandi_, Mar 18 2011: (Start)
%F a(n) = 40*a(n-1) - 593*a(n-2) + 3854*a(n-3) - 9240*a(n-4), n >= 4.
%F a(n) = 23*a(n-1) - 132*a(n-2) + (10^(n+1) - 7^(n+1))/3, n >= 2. (End)
%F a(n) = 6*12^(n+2)/5 - 11^(n+3)/4 + 5*10^(n+2)/3 - 7^(n+3)/60. - _R. J. Mathar_, Mar 20 2011
%t CoefficientList[Series[1/((1-7x)(1-10x)(1-11x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{40,-593,3854,-9240},{1,40,1007,20414},30] (* _Harvey P. Dale_, Jun 03 2023 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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