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%I #16 Sep 08 2022 08:46:19
%S 0,0,0,2,15,75,319,1256,4754,17624,64613,235465,855293,3101198,
%T 11233632,40670374,147200107,532681447,1927472251,6974085108,
%U 25233326446,91296730996,330318071345,1195108798917,4323957832185,15644253554970,56601495391164,204786242735426,740923803830199
%N Expansion of x^3*(2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)).
%H Vincenzo Librandi, <a href="/A283842/b283842.txt">Table of n, a(n) for n = 0..1000</a>
%H Esther M. Banaian, <a href="http://digitalcommons.csbsju.edu/honors_thesis/24">Generalized Eulerian Numbers and Multiplex Juggling Sequences</a>, (2016). All College Thesis Program. Paper 24. See p. 29.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-30,47,-35,10).
%F G.f.: x^3*(2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)).
%F a(n) = 2 - 2^n + (2^(-1-n)*(-(5-sqrt(5))^n*(3+sqrt(5)) - (-3+sqrt(5))*(5+sqrt(5))^n)) / sqrt(5) + n. - _Colin Barker_, Mar 29 2017
%t CoefficientList[Series[x^3 (2 - 3 x)/((1 - x)^2 (1 - 2 x) (1 - 5 x + 5 x^2)), {x, 0, 33}], x] (* _Vincenzo Librandi_, Mar 29 2017 *)
%t LinearRecurrence[{9,-30,47,-35,10},{0,0,0,2,15},30] (* _Harvey P. Dale_, Aug 29 2022 *)
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0,0,0] cat Coefficients(R!((2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)))); // _Vincenzo Librandi_, Mar 29 2017
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Mar 28 2017
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