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%I #25 Sep 08 2022 08:44:46
%S 1,23,350,4450,51231,554433,5756260,58034900,572630861,5558653243,
%T 53279890170,505596134550,4759287370891,44506489496453,
%U 413949260130080,3832708325439400,35351885537967321,325028008388124063,2980145152236043990,27260474825925725450,248857740289031716151
%N Expansion of 1/((1-x)*(1-5*x)*(1-8*x)*(1-9*x)).
%H Vincenzo Librandi, <a href="/A022469/b022469.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 (23,-179,517,-360).
%F a(n) = (21*9^(n+3)-32*8^(n+3)+14*5^(n+3)-3)/672. - _Yahia Kahloune_, May 25 2013
%F a(0)=1, a(1)=23, a(2)=350, a(3)=4450; for n>3, a(n) = 23*a(n-1) -179*a(n-2) +517*a(n-3) -360*a(n-4). - _Vincenzo Librandi_, Jul 12 2013
%t CoefficientList[Series[1/((1-x)*(1-5*x)*(1-8*x)*(1-9*x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)
%t LinearRecurrence[{23,-179,517,-360},{1,23,350,4450},20] (* _Harvey P. Dale_, Feb 28 2015 *)
%o (Magma) I:=[1, 23, 350, 4450]; [n le 4 select I[n] else 23*Self(n-1)-179*Self(n-2)+517*Self(n-3)-360*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)*(1-9*x)))); // _Vincenzo Librandi_, Jul 12 2013
%o (PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-8*x)*(1-9*x))) \\ _G. C. Greubel_, Feb 27 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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