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%I #16 May 23 2023 12:13:13
%S 1,23,368,5098,65559,806541,9640606,112964816,1304876837,14914020979,
%T 169097614764,1905464222454,21368620595635,238731453906137,
%U 2659135639187642,29548298847110812,327711548662770753
%N Expansion of 1/((1-x)(1-2x)(1-9x)(1-11x)).
%H Vincenzo Librandi, <a href="/A021294/b021294.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,-161,337,-198).
%F G.f.: 1/((1-x)(1-2x)(1-9x)(1-11x)).
%F a(n) = (28*11^(n+3) - 45*9^(n+3) + 80*2^(n+3) - 63)/5040. [_Yahia Kahloune_, Jul 08 2013]
%F a(0)=1, a(1)=23, a(2)=368, a(3)=5098; for n>3, a(n) = 23*a(n-1) -161*a(n-2) +337*a(n-3) -198*a(n-4). - _Vincenzo Librandi_, Jul 08 2013
%F a(0)=1, a(1)=23; for n>1, a(n) = 20*a(n-1) -99*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)
%o (Magma) I:=[1,23,368,5098]; [n le 4 select I[n] else 23*Self(n-1)-161*Self(n-2)+337*Self(n-3)-198*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-9*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 08 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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