

A180400


Coefficients of Maclaurin series for (19x9x^2)^(1/3).


2



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

0,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200


FORMULA

G.f.: (19x9x^2)^(1/3).
Recurrence: n*a(n) = 3*(3*n2)*a(n1) + 3*(3*n4)*a(n2).  Vaclav Kotesovec, Oct 20 2012
a(n) ~ sqrt(3)*Gamma(2/3)/(2^(2/3)*(133*sqrt(13))^(1/3)*Pi) * ((9+3*sqrt(13))/2)^n/(n^(2/3)).  Vaclav Kotesovec, Oct 20 2012


EXAMPLE

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


MATHEMATICA

CoefficientList[Series[Power[19x9x^2, (3)^1], {x, 0, 20}], x] (* Harvey P. Dale, Mar 11 2012 *)


CROSSREFS

Cf. A180399.
Sequence in context: A074570 A136781 A225439 * A166696 A058194 A179815
Adjacent sequences: A180397 A180398 A180399 * A180401 A180402 A180403


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Sep 01 2010, Sep 02 2010


STATUS

approved



