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A371644
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a(n) = Product_{k=0..n} binomial(n^2 + k^2, n^2 - k^2).
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0
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c * exp(Pi*n^3/3 + Pi*n/4 + n) / (2^(2*n^3/3 + 3*n/2) * Pi^(n/2) * A^(2*n) * n^(7*n/6 - 1/4)), where c = 0.761512... = 2^(1/4) * A255504 * (c from A371603) / (c from A371645) and A is the Glaisher-Kinkelin constant A074962.
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MATHEMATICA
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Table[Product[Binomial[n^2+k^2, n^2-k^2], {k, 0, n}], {n, 0, 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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STATUS
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approved
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