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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
OFFSET
0,4
LINKS
Esther M. Banaian, Generalized Eulerian Numbers and Multiplex Juggling Sequences, (2016). All College Thesis Program. Paper 24. See p. 29.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 28 2017
STATUS
approved