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A051675
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"Second factorials": Product_{k=1..n} k^(k^2).
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18
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OFFSET
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1,2
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REFERENCES
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Spyros G. Kanellos: Mathematical Researches and Results [in Greek]. Athens, 1965.
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LINKS
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FORMULA
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a(n) ~ n^(n*(n+1)*(2n+1)/6) / exp(n^3/9 - n/12 - Zeta(3)/(4*Pi^2)), where Zeta(3) = A002117 = 1.2020569031595942853997... . - Vaclav Kotesovec, Feb 20 2015
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MAPLE
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A051675 := proc(n) local k; mul(k^(k^2), k=1..n); end;
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MATHEMATICA
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Table[Product[k^(k^2), {k, 1, n}], {n, 1, 10}] (* Vaclav Kotesovec, Feb 20 2015 *)
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PROG
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(PARI) for(n=1, 10, print1(prod(k=1, n, k^(k^2)), ", ")) \\ G. C. Greubel, Oct 14 2018
(Magma) [(&*[k^(k^2): k in [1..n]]): n in [1..10]]; // G. C. Greubel, Oct 14 2018
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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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STATUS
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approved
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