OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
Recurrence: n*a(n) = 3*(9*n-4)*a(n-1) - 54*(3*n-2)*a(n-2). - Vaclav Kotesovec, Oct 14 2012
a(n) ~ 2/Gamma(1/3)*18^n/n^(2/3). - Vaclav Kotesovec, Oct 14 2012
G.f.: 1/((1-9*x)*(1-18*x)^(1/3)). - Vaclav Kotesovec, Oct 21 2012
EXAMPLE
a(3)=2871
MATHEMATICA
f[n_] := 3^(2n)* Integrate[(1 + x^3)^n, {x, 0, 1}]/Integrate[(1 - x^3)^n, {x, 0, 1}]; Table[ f[n], {n, 0, 18}] (* Robert G. Wilson v, Dec 22 2003 *)
CoefficientList[Series[1/((1-9*x)*(1-18*x)^(1/3)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 21 2012 *)
Table[3^(2*n)*Sum[2^k/(3^k*k!)*Product[3*j-2, {j, 1, k}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2012 *)
PROG
(PARI) x='x+O('x^66); Vec(1/((1-9*x)*(1-18*x)^(1/3))) \\ Joerg Arndt, May 10 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)excite.com), Dec 05 2003
EXTENSIONS
More terms from Robert G. Wilson v, Dec 22 2003
STATUS
approved