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%I #18 Sep 08 2022 08:44:40
%S 1,17,218,2554,28875,321531,3556372,39217748,431883509,4753160005,
%T 52296967086,575327673102,6328909579903,69619531257839,
%U 765822473230760,8424085352511016,92665129612484457,1019317379411645433,11212495941899681794,123337479202754409890
%N Expansion of 1/((1-x)*(1-5*x)*(1-11*x)).
%H Vincenzo Librandi, <a href="/A016238/b016238.txt">Table of n, a(n) for n = 0..970</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-71,55).
%F a(n) = 16*a(n-1) - 55*a(n-2) + 1 for n>1, a(0)=1, a(1)=17. - _Vincenzo Librandi_, Feb 10 2011
%F a(n) = 17*a(n-1) - 71*a(n-2) + 55*a(n-3). - _Vincenzo Librandi_, Aug 23 2018
%F a(n) = (2*11^(n+2) - 5^(n+3) + 3)/120. - _Bruno Berselli_, Aug 23 2018
%t CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 23 2018 *)
%t Table[(2 11^(n + 2) - 5^(n + 3) + 3)/120, {n, 0, 20}] (* _Bruno Berselli_, Aug 23 2018 *)
%o (Magma) I:=[1,17]; [n le 2 select I[n] else 16*Self(n-1)-55*Self(n-2)+1: n in [1..30]]; // _Vincenzo Librandi_, Aug 23 2018
%o (Magma) [(2*11^(n+2)-5^(n+3)+3)/120: n in [0..20]]; // _Bruno Berselli_, Aug 23 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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