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A089138
a(n) = (3^(2*n))*(integral_{x=0 to 1} (1+x^3)^n dx)/(integral_{x=0 to 1} (1-x^3)^n dx).
1
1, 15, 207, 2871, 40959, 604503, 9214479, 144391815, 2313641151, 37724683959, 623474304111, 10412641429479, 175337108637471, 2971909404000279, 50642191943368911, 866773853177022279, 14890613346688811391
OFFSET
0,2
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
Sequence in context: A063906 A194481 A078265 * A271333 A051813 A280160
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

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Last modified September 20 16:06 EDT 2024. Contains 376074 sequences. (Running on oeis4.)