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A263430
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a(n) = Product_{k=0..n} (4*k+1)^(n-k).
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1
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1, 1, 5, 225, 131625, 1309010625, 273380323978125, 1427352844030287890625, 216119240915841469025244140625, 1079864992142473709995957417730712890625, 199639840782299404795675492100337942688751220703125
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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) ~ A^(1/8) * 2^(n^2 + 3*n/2 + 1/8) * Pi^(n/2 + 1/8) * n^(n^2/2 + n/4 - 5/96) / (Gamma(1/4)^(n + 1/4) * exp(3*n^2/4 + n/4 + 1/96 - C/(4*Pi))), where A = A074962 is the Glaisher-Kinkelin constant and C = A006752 = is Catalan's constant.
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MATHEMATICA
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Table[Product[(4*k+1)^(n-k), {k, 0, n}], {n, 0, 10}]
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PROG
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(PARI) for(n=0, 10, print1(prod(k=0, n, (4*k+1)^(n-k)), ", ")) \\ G. C. Greubel, Aug 25 2018
(Magma) [(&*[(4*k+1)^(n-k): k in [0..n]]): n in [0..10]]; // G. C. Greubel, Aug 25 2018
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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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