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A371339
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a(n) = Product_{k=1..n} A000178(k)^k.
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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) = Product_{k=1..n} BarnesG(k+2)^k.
a(n) ~ (2*Pi)^(n*(n+1)*(n+2)/6) * n^(n^4/8 + 7*n^3/12 + 5*n^2/6 + 3*n/8 + 19/720) / (A^(n^2/2 + n/2 - 1/3) * exp(7*n^4/32 + 59*n^3/72 + 17*n^2/24 - n/24 + zeta(3)/(8*Pi^2) + zeta'(-3)/6 - 37/720)), where A is the Glaisher-Kinkelin constant A074962, zeta(3) = A002117, zeta'(-3) = A259068.
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MATHEMATICA
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Table[Product[BarnesG[k+2]^k, {k, 1, 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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