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%I #10 Feb 20 2015 09:52:52
%S 1,4,1728,6879707136,49302469038676377600000,
%T 237376313799769806328950291431424000000000000,
%U 487929826521303413461947888047619993419888153407795494912000000000000000000000
%N a(n) = Product_{k=1..n} k!^n.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Superfactorial.html">Superfactorial</a>
%F a(n) = A000178(n)^n.
%F a(n) ~ exp(1/12 + n/12 - n^2 - 3*n^3/4) * n^(5*n/12 + n^2 + n^3/2) * 2^(n/2 + n^2/2) * Pi^(n/2 + n^2/2) / A^n, where A = 1.28242712910062263687534256886979... is the Glaisher-Kinkelin constant (see A074962).
%t Table[Product[k!,{k,1,n}]^n,{n,1,10}]
%t Table[BarnesG[n+2]^n, {n, 1, 10}]
%Y Cf. A000178, A055462, A074962, A255269.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Feb 20 2015
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