OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: (1-9x-9x^2)^(-1/3).
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
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
a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(k,n-k). - Seiichi Manyama, Mar 27 2023
EXAMPLE
The Maclaurin series begins with 1 + 3x + 21x^2.
MATHEMATICA
CoefficientList[Series[Power[1-9x-9x^2, (-3)^-1], {x, 0, 20}], x] (* Harvey P. Dale, Mar 11 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 01 2010, Sep 02 2010
STATUS
approved