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A367492
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a(n) = Product_{k=0..n} (k+1)!^k.
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2
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1, 2, 72, 995328, 206391214080000, 39934999921327865856000000000, 654541076770994951831125144608178176000000000000000, 113391518341540395635327816456127297986876881699306137641287680000000000000000000000
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ A^(3/2) * n^(n^3/3 + 5*n^2/4 + 11*n/12 - 3/8) * (2*Pi)^(n^2/4 + n/4 - 1/2) / exp(4*n^3/9 + 7*n^2/8 - n + zeta(3)/(8*Pi^2) - 25/24), where A is the Glaisher-Kinkelin constant A074962.
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MATHEMATICA
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Table[Product[(k+1)!^k, {k, 0, n}], {n, 0, 10}]
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PROG
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(Magma) [(&*[Factorial(k+1)^k: k in [0..n]]): n in [0..15]]; // G. C. Greubel, Feb 18 2024
(SageMath) [product(factorial(k+1)^k for k in range(n+1)) for n in range(16)] # G. C. Greubel, Feb 18 2024
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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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