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 A180400 Coefficients of Maclaurin series for (1-9x-9x^2)^(-1/3). 2

%I

%S 1,3,21,162,1341,11529,101619,911466,8281737,76002381,703017549,

%T 6544803564,61254970686,575885086182,5434948357146,51462813578148,

%U 488705091057981,4652700300002475,44395945025504625,424479488258350350

%N Coefficients of Maclaurin series for (1-9x-9x^2)^(-1/3).

%H Vincenzo Librandi, <a href="/A180400/b180400.txt">Table of n, a(n) for n = 0..200</a>

%F G.f.: (1-9x-9x^2)^(-1/3).

%F D-finite with recurrence: n*a(n) = 3*(3*n-2)*a(n-1) + 3*(3*n-4)*a(n-2). - _Vaclav Kotesovec_, Oct 20 2012

%F 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

%e The Maclaurin series begins with 1 + 3x + 21x^2.

%t CoefficientList[Series[Power[1-9x-9x^2, (-3)^-1],{x,0,20}],x] (* _Harvey P. Dale_, Mar 11 2012 *)

%Y Cf. A180399.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Sep 01 2010, Sep 02 2010

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Last modified May 25 07:29 EDT 2020. Contains 334584 sequences. (Running on oeis4.)