A283842 Expansion of x^3*(2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)).

0, 0, 0, 2, 15, 75, 319, 1256, 4754, 17624, 64613, 235465, 855293, 3101198, 11233632, 40670374, 147200107, 532681447, 1927472251, 6974085108, 25233326446, 91296730996, 330318071345, 1195108798917, 4323957832185, 15644253554970, 56601495391164, 204786242735426, 740923803830199

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Esther M. Banaian, Generalized Eulerian Numbers and Multiplex Juggling Sequences, (2016). All College Thesis Program. Paper 24. See p. 29.

Index entries for linear recurrences with constant coefficients, signature (9,-30,47,-35,10).

Formula

G.f.: x^3*(2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)).

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

Mathematica

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 *)
LinearRecurrence[{9, -30, 47, -35, 10}, {0, 0, 0, 2, 15}, 30] (* Harvey P. Dale, Aug 29 2022 *)

Prog

(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

Crossrefs

Sequence in context: A007232 A308914 A099743 * A344215 A102289 A041243

Adjacent sequences: A283839 A283840 A283841 * A283843 A283844 A283845

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 28 2017

Status

approved