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A058808
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Product{k=1 to n}[S(n,k)], where S(n,k) is a Stirling number of the second kind. (S(n,k) = number of ways of partitioning a set of n elements into k nonempty subsets.)
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5
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1, 1, 3, 42, 3750, 2720250, 19512927000, 1631977354072800, 1833446251541145780000, 31323109023670061678062500000, 9087660958278168844264470405352500000
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OFFSET
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1,3
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LINKS
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FORMULA
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log(a(n)) ~ n^2 * (log(n) + gamma - 3/2) / 2, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 27 2021
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EXAMPLE
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a(4) = S(4,1)*S(4,2)*S(4,3)*S(4,4) = 1*7*6*1 = 42.
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MAPLE
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a:=n->mul(stirling2(n, k), k=1..n): seq(a(n), n=1..12); # Zerinvary Lajos, Jun 28 2007
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MATHEMATICA
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Table[Product[StirlingS2[n, k], {k, 1, n}], {n, 1, 12}] (* Vaclav Kotesovec, Feb 26 2021 *)
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PROG
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(PARI) a(n) = prod(k=1, n, stirling(n, k, 2)); \\ Michel Marcus, Dec 12 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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