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A283842 Expansion of x^3*(2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)). 1
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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: A178321 A007232 A099743 * A102289 A041243 A216247

Adjacent sequences:  A283839 A283840 A283841 * A283843 A283844 A283845

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 28 2017

STATUS

approved

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Last modified December 19 11:13 EST 2018. Contains 318246 sequences. (Running on oeis4.)