%I #21 Sep 08 2022 08:44:46
%S 1,25,416,5810,73731,881895,10139746,113382280,1242174461,13399350965,
%T 142804173876,1507398751950,15788505813991,164317248669235,
%U 1701069830850806,17531812552906820,180008344463520321
%N Expansion of 1/((1-x)*(1-5*x)*(1-9*x)*(1-10*x)).
%H Vincenzo Librandi, <a href="/A022845/b022845.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 (25,-209,635,-450).
%F a(n) = (32*10^(n+3) - 45*9^(n+3) + 18*5^(n+3) - 5)/1440. - _Yahia Kahloune_, Jun 29 2013
%F a(0)=1, a(1)=25, a(2)=416, a(3)=5810; for n>3, a(n) = 25*a(n-1) -209*a(n-2) +635*a(n-3) -450*a(n-4). - _Vincenzo Librandi_, Jul 12 2013
%p seq(coeff(series(((1-x)*(1-5*x)*(1-9*x)*(1-10*x))^(-1),x,n+1), x, n), n = 0..20); # _Muniru A Asiru_, Sep 28 2018
%t CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-9*x)*(1-10*x)))); /* or /* I:=[1, 25, 416, 5810]; [n le 4 select I[n] else 25*Self(n-1)-209*Self(n-2)+635*Self(n-3)-450*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 12 2013
%o (PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-9*x)*(1-10*x))) \\ _G. C. Greubel_, Sep 28 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_