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A159783
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Hankel transform of ordered Bell numbers A000670. a(n)=det(A000670(i+j-1)), i,j=1,2..n.
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1
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 2^((n-1)*n/2)*G(n+1)*G(n+2)=2^((n-1)*n/2)*A000178(n-1)*A000178(n), where G(n)=product(Gamma(k), k=1..n). - Todd Silvestri, Nov 15 2014
a(n) ~ 2^((n^2 + n + 1)/2) * n^(n^2 + n + 1/3) * Pi^(n + 1/2) / (A^2 * exp(3*n^2/2 + n - 1/6)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 10 2015
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MATHEMATICA
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a[n_Integer/; n>=1]:=2^((n-1) n/2) BarnesG[n+1] BarnesG[n+2] (* Todd Silvestri, Nov 15 2014 *)
a[n_] := Table[HurwitzLerchPhi[1/2, 1-i-j, 0]/2, {i, n}, {j, n}] // Det;
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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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