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A324596
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a(n) = n!^(3*n) * Product_{k=1..n} binomial(n + 1/k^2, n).
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2
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1, 2, 270, 74692800, 419731620267960000, 252716802910471719823692648960000, 59736659298524125157504488525739821430187940800000000, 16079377413231597423103950774423398920424350187193326745026311068057600000000000
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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) ~ n!^(3*n) * n^(Pi^2/6) / A303670.
a(n) ~ n^(3*n*(2*n+1)/2 + Pi^2/6) * (2*Pi)^(3*n/2) / exp(3*n^2 - 1/4 - gamma*Pi^2/6 + c), where gamma is the Euler-Mascheroni constant A001620 and c = A306774 = Sum_{k>=2} (-1)^k * Zeta(k) * Zeta(2*k) / k.
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MAPLE
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a:= n-> n!^(3*n)*mul(binomial(n+1/k^2, n), k=1..n):
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MATHEMATICA
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Table[n!^(3*n) * Product[Binomial[n + 1/k^2, n], {k, 1, n}], {n, 1, 8}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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