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A188681
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a(n) = binomial(3n,n)^2/(2n+1).
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11
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1, 3, 45, 1008, 27225, 819819, 26509392, 901402560, 31818681873, 1156122556875, 42985853635725, 1628541825580800, 62667882587091600, 2443473892345873968, 96351855806554401600, 3836565846094702507776, 154071018890153214025473
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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: 4*(n+1)^2*(2*n+1)*(2*n+3)*a(n+1)-9*(3*n+1)^2*(3*n+2)^2*a(n)=0.
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MATHEMATICA
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Table[Binomial[3k, k]^2/(2k+1), {k, 0, 20}}.
CoefficientList[Series[HypergeometricPFQ[{1/3, 1/3, 2/3, 2/3}, {1/2, 1, 3/2}, (729 x)/16], {x, 0, 20}], x] (* Harvey P. Dale, Apr 22 2011 *)
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PROG
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(Maxima) makelist(binomial(3*k, k)^2/(2*k+1), k, 0, 20);
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CROSSREFS
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Cf. A005809, A001764, A188676, A104859, A188678, A188679, A188680, A188682, A188683, A188684, A188685, A188686, A188687.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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