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A366306
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a(n) = Product_{k=1..n} (k^n - (k-1)^n).
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1
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1, 3, 133, 170625, 10733002621, 50465283999665535, 25145494699347449245677097, 1787473773567267792523164108726890625, 23480751910878672340765325385856840967957995534681, 71672834655019406921956925590632596034005848922160549420728589375
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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) = (n!)^n * Product_{k=1..n} (1 - (1 - 1/k)^n).
a(n) ~ n!^n * d^n, where d = exp(Integral_{x=0..1} log(1 - exp(-1/x)) dx) = 0.84207793096051704199642805288991601369639823969574423397520945175552718...
a(n) ~ (2*Pi)^(n/2) * d^n * n^(n*(2*n+1)/2) / exp(n^2 - 1/12).
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MATHEMATICA
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Table[Product[k^n - (k-1)^n, {k, 1, n}], {n, 1, 10}]
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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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