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A191510
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Product of terms in n-th row of A132818.
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0
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1, 9, 648, 360000, 1518750000, 48243443062500, 11480517255997440000, 20400479323264014247526400, 270090559531318533654528000000000, 26599911685677709861296622500000000000000, 19464564507161243794359748945629699456000000000000
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OFFSET
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1,2
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COMMENTS
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Lim_{n -> inf} (a(n)*a(n+2))/a(n+1)^2 = e^2. Like A168510, this limit is asymptotic from above.
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LINKS
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FORMULA
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a(n)=product[product[((k + 1)/(k - 1))^k, {k, 2, j}], {j, 1, n}].
a(n) ~ A^4 * exp(n^2 + 2*n + 5/6) / (n^(2/3) * 2^(2*n+1) * Pi^(n+1)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 11 2015
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EXAMPLE
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For n=3, row 3 of A132818 = {6,18,6} and a(3)=648.
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MATHEMATICA
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Table[Product[Product[((k + 1)/(k - 1))^k, {k, 2, j}], {j, 1, n}], {n, 1, 11}]
Table[(n + 1)^n * Hyperfactorial[n]^2 / (2^n * BarnesG[n+2]^2), {n, 1, 12}] (* Vaclav Kotesovec, Jul 11 2015 *)
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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STATUS
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approved
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