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A324590
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a(n) = n!^(4*n) * Product_{k=1..n} binomial(n + 1/k^2, n).
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2
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1, 2, 1080, 16133644800, 139256878046022696960000, 6288402750181849898716908922601472000000000, 8322157105451357856813375261666887975745751468393837363200000000000000
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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!^(4*n) * n^(Pi^2/6) / A303670.
a(n) ~ n^(4*n^2 + 2*n + Pi^2/6) * (2*Pi)^(2*n) / exp(4*n^2 - 1/3 - 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!^(4*n)*mul(binomial(n+1/k^2, n), k=1..n):
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MATHEMATICA
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Table[n!^(4*n) * Product[Binomial[1/k^2 + n, 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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