%I #21 Sep 08 2022 08:44:46
%S 1,24,383,5130,62481,718164,7948003,85708590,907402661,9479002104,
%T 98042032023,1006497443250,10273896592441,104411869082844,
%U 1057509545490443,10682260439173110,107680115000743821
%N Expansion of 1/((1-x)*(1-5*x)*(1-8*x)*(1-10*x)).
%H Vincenzo Librandi, <a href="/A022565/b022565.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 (24,-193,570,-400).
%F a(n) = (14*10^(n+3) - 30*8^(n+3) + 21*5^(n+3) -5)/1260. - _Yahia Kahloune_, Jul 01 2013
%F a(0)=1, a(1)=24, a(2)=383, a(3)=5130; for n>3, a(n) = 24*a(n-1) -193*a(n-2) +570*a(n-3)-400*a(n-4). - _Vincenzo Librandi_, Jul 12 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)
%o (Magma) I:=[1, 24, 383, 5130]; [n le 4 select I[n] else 24*Self(n-1)-193*Self(n-2)+570*Self(n-3)-400*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-8*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 12 2013
%o (PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-8*x)*(1-10*x))) \\ _G. C. Greubel_, Feb 26 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_