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A091004
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Expansion of x*(1-x)/((1-2*x)*(1+3*x)).
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6
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0, 1, -2, 8, -20, 68, -188, 596, -1724, 5300, -15644, 47444, -141308, 425972, -1273820, 3829652, -11472572, 34450484, -103285916, 309988820, -929704316, 2789637236, -8367863132, 25105686548, -75312865340, 225946984628, -677824176668, 2033506084436
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OFFSET
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0,3
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COMMENTS
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Inverse binomial transform of A091001.
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LINKS
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FORMULA
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G.f.: x*(1-x)/((1-2*x)*(1+3*x)).
a(n) = (3*2^n - 8*(-3)^n + 5*0^n)/30.
E.g.f.: (3*exp(2*x) - 8*exp(-3*x) + 5)/30. - G. C. Greubel, Feb 01 2019
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MATHEMATICA
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CoefficientList[Series[x(1-x)/((1-2x)(1+3x)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jan 17 2017 *)
Join[{0}, LinearRecurrence[{-1, 6}, {1, -2}, 30]] (* G. C. Greubel, Feb 01 2019 *)
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PROG
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(PARI) vector(30, n, n--; (3*2^n - 8*(-3)^n + 5*0^n)/30) \\ G. C. Greubel, Feb 01 2019
(Magma) [0] cat [(3*2^n - 8*(-3)^n)/30: n in [1..30]]; // G. C. Greubel, Feb 01 2019
(Sage) [0] + [(3*2^n - 8*(-3)^n)/30 for n in (1..30)] # G. C. Greubel, Feb 01 2019
(GAP) Concatenation([0], List([1..30], n -> (3*2^n - 8*(-3)^n)/30)) # G. C. Greubel, Feb 01 2019
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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