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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 *) LinearRecurrence[{9, -30, 47, -35, 10}, {0, 0, 0, 2, 15}, 30] (* Harvey P. Dale, Aug 29 2022 *) PROG (Magma) m:=30; R:=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

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Last modified August 4 17:35 EDT 2024. Contains 374923 sequences. (Running on oeis4.)