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A272167
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a(n) = Product_{k=2..n} (k^2-k)^k.
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1
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1, 4, 864, 17915904, 57330892800000, 41794220851200000000000, 9635211808655307020697600000000000, 931891782579353562478377930946353561600000000000, 48457159197906991133853954271145046614004301737177907200000000000
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) ~ A^2 * sqrt(2*Pi) * n^(n^2 + n - 1/3) / exp(n*(n+2)/2), where A = A074962 is the Glaisher-Kinkelin constant.
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MATHEMATICA
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Table[Product[(k^2-k)^k, {k, 2, n}], {n, 1, 10}]
Table[n^n * Gamma[n]^(2*n-1) / BarnesG[n]^2, {n, 1, 10}] (* Vaclav Kotesovec, Apr 21 2024 *)
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PROG
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(PARI) a(n) = prod(k=2, n, (k^2-k)^k); \\ Michel Marcus, Nov 18 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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