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A324589
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a(n) = Product_{j=1..n, k=1..n} (1 + (j*k)^2).
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3
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OFFSET
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0,2
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COMMENTS
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Product_{j>=1, k>=1} (1 + 1/(j^3*k^3)) = 3.07044599622955113359633939413741321690850038945774000273914990604256664558...
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LINKS
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FORMULA
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a(n) ~ c * 4^n * Pi^(2*n) * n^(2*n*(2*n+1)) / exp(4*n^2), where c = 14.2467190172413789737182639605567415110439648274273645215657580983939589... = exp(1/3) * Product_{j>=1, k>=1} (1 + 1/(j^2*k^2)). - Vaclav Kotesovec, Mar 28 2019
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MAPLE
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a:= n-> mul(mul((i*j)^2+1, i=1..n), j=1..n):
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MATHEMATICA
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Table[Product[j^2*k^2 + 1, {j, 1, n}, {k, 1, n}], {n, 1, 8}]
Round[Table[Product[k^(1 + 2*n) * Gamma[1 - I/k + n] * Gamma[1 + I/k + n] * Sinh[Pi/k]/Pi, {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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