%I #17 Nov 25 2024 17:51:01
%S 1,26,452,6622,88473,1117788,13616464,161765924,1887776825,
%T 21743151430,247985329956,2807195642706,31593670364257,
%U 353962564536152,3951485554056128,43987455339016168,488552227663629969
%N Expansion of 1/((1-x)(1-5x)(1-9x)(1-11x)).
%H Vincenzo Librandi, <a href="/A023540/b023540.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (26,-224,694,-495).
%F a(n) = (8*11^(n+3) - 15*9^(n+3) + 10*5^(n+3) - 3)/960. [_Yahia Kahloune_, Jun 29 2013]
%F a(0)=1, a(1)=26, a(2)=452, a(3)=6622; for n>3, a(n) = 26*a(n-1) -224*a(n-2) +694*a(n-3) -495*a(n-4). - _Vincenzo Librandi_, Jul 12 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)
%o (Magma) I:=[1,26,452,6622]; [n le 4 select I[n] else 26*Self(n-1)-224*Self(n-2)+694*Self(n-3)-495*Self(n-4): n in [1..25]]; // _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)*(1-11*x)))); // _Vincenzo Librandi_, Jul 12 2013
%K nonn,easy,changed
%O 0,2
%A _N. J. A. Sloane_