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A268196
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a(n) = Product_{k=0..n} binomial(3*k,k).
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13
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1, 3, 45, 3780, 1871100, 5618913300, 104309506501200, 12129109415959536000, 8920608231265175901456000, 41809329673499408044341517200000, 1256161937180234817183361549396758000000, 243113461110708695347467432844366521953760000000
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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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a(n) = A^(7/6) * Gamma(1/3)^(1/3) * 3^(3*n^2/2 + 2*n + 11/36)* BarnesG(n + 4/3) * BarnesG(n + 5/3) / (exp(7/72) * 2^(n^2 + 2*n + 5/8) * Pi^(n/2 + 5/12) * BarnesG(n + 3/2) * BarnesG(n + 2)), where A = A074962 is the Glaisher-Kinkelin constant.
a(n) ~ A^(7/6) * Gamma(1/3)^(1/3) * 3^(11/36 + 2*n + 3*n^2/2) * exp(n/2 - 7/72) / (2^(n^2 + 2*n + 7/8) * Pi^(n/2 + 2/3) * n^(n/2 + 25/72)), where A = A074962 is the Glaisher-Kinkelin constant.
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MATHEMATICA
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Table[Product[Binomial[3k, k], {k, 0, n}], {n, 0, 12}]
FoldList[Times, Table[Binomial[3n, n], {n, 0, 15}]] (* Harvey P. Dale, Apr 23 2018 *)
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CROSSREFS
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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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