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A372150
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a(n) = Product_{k=1..n} k!^(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) ~ (2*Pi)^(n^3/6 + n^2/4 + n/12) * n^(n^4/4 + 2*n^3/3 + n^2/2 + n/12 - 1/90) / (A^(1/6) * exp(5*n^4/16 + 5*n^3/9 + n^2/8 - n/12 - zeta(3)/(8*Pi^2) - zeta'(-3)/3 - 13/720)), 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[k!^(k^2), {k, 1, n}], {n, 0, 6}]
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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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