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A180400
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Coefficients of Maclaurin series for (1-9x-9x^2)^(-1/3).
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2
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1, 3, 21, 162, 1341, 11529, 101619, 911466, 8281737, 76002381, 703017549, 6544803564, 61254970686, 575885086182, 5434948357146, 51462813578148, 488705091057981, 4652700300002475, 44395945025504625, 424479488258350350
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OFFSET
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0,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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G.f.: (1-9x-9x^2)^(-1/3).
Recurrence: n*a(n) = 3*(3*n-2)*a(n-1) + 3*(3*n-4)*a(n-2). - Vaclav Kotesovec, Oct 20 2012
a(n) ~ sqrt(3)*Gamma(2/3)/(2^(2/3)*(13-3*sqrt(13))^(1/3)*Pi) * ((9+3*sqrt(13))/2)^n/(n^(2/3)). - Vaclav Kotesovec, Oct 20 2012
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EXAMPLE
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The Maclaurin series begins with 1 + 3x + 21x^2.
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MATHEMATICA
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CoefficientList[Series[Power[1-9x-9x^2, (-3)^-1], {x, 0, 20}], x] (* From Harvey P. Dale, Mar 11 2012 *)
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CROSSREFS
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Cf. A180399.
Sequence in context: A074570 A136781 A225439 * A166696 A058194 A179815
Adjacent sequences: A180397 A180398 A180399 * A180401 A180402 A180403
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Sep 01 2010, Sep 02 2010
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STATUS
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approved
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