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A089138
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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).
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1
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1, 15, 207, 2871, 40959, 604503, 9214479, 144391815, 2313641151, 37724683959, 623474304111, 10412641429479, 175337108637471, 2971909404000279, 50642191943368911, 866773853177022279, 14890613346688811391
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OFFSET
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0,2
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LINKS
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FORMULA
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Recurrence: n*a(n) = 3*(9*n-4)*a(n-1) - 54*(3*n-2)*a(n-2). - Vaclav Kotesovec, Oct 14 2012
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EXAMPLE
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a(3)=2871
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MATHEMATICA
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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 *)
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PROG
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(PARI) x='x+O('x^66); Vec(1/((1-9*x)*(1-18*x)^(1/3))) \\ Joerg Arndt, May 10 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)excite.com), Dec 05 2003
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EXTENSIONS
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STATUS
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approved
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