Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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_