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%I #12 Mar 30 2016 04:27:45
%S 1,4,192,221184,10192158720,28179280429056000,
%T 6544446260541338419200000,170229151878929266676890337280000000,
%U 637613431509979741286846928045094207488000000000
%N Hankel transform of ordered Bell numbers A000670. a(n)=det(A000670(i+j-1)), i,j=1,2..n.
%H Todd Silvestri, <a href="/A159783/b159783.txt">Table of n, a(n) for n = 1..30</a>
%F 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
%F 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
%t a[n_Integer/;n>=1]:=2^((n-1) n/2) BarnesG[n+1] BarnesG[n+2] (* _Todd Silvestri_, Nov 15 2014 *)
%t a[n_] := Table[HurwitzLerchPhi[1/2, 1-i-j, 0]/2, {i, n}, {j, n}] // Det;
%t Array[a, 10] (* _Jean-François Alcover_, Mar 30 2016 *)
%K nonn
%O 1,2
%A _Karol A. Penson_, Apr 22 2009