%I #21 Aug 18 2018 18:27:07
%S 1,22,323,4004,45465,491106,5149327,53020528,539857109,5458923470,
%T 54963556011,551942523132,5533572185233,55422129454714,
%U 554747369555975,5550668292585416,55526041242871437,555377516005134438
%N Expansion of 1/((1-x)*(1-5*x)*(1-6*x)*(1-10*x)).
%H G. C. Greubel, <a href="/A022343/b022343.txt">Table of n, a(n) for n = 0..995</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-161,440,-300).
%F a(n) = (1/180)*(9*5^(n+3) + 10^(n+3) - 9*6^(n+3) - 1). - _R. J. Mathar_, Mar 11 2011
%F a(n) = 16*a(n-1) - 60*a(n-2) + (5^(n+1) - 1)/4, n>=2. - _Vincenzo Librandi_, Mar 12 2011
%F E.g.f.: (1/180)*(- exp(x) + 1125*exp(5*x) - 1944*exp(6*x) + 1000*exp(10*x)). - _G. C. Greubel_, Aug 25 2017
%t Table[(1/180)*(9*5^(n + 3) + 10^(n + 3) - 9*6^(n + 3) - 1), {n,0,50}] (* _G. C. Greubel_, Aug 25 2017 *)
%t CoefficientList[Series[1/((1-x)(1-5x)(1-6x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{22,-161,440,-300},{1,22,323,4004},30] (* _Harvey P. Dale_, Aug 18 2018 *)
%o (PARI) Vec(1/(1-x)/(1-5*x)/(1-6*x)/(1-10*x)+O(x^99)) \\ _Charles R Greathouse IV_, Dec 22 2011
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_