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%I #7 Apr 23 2016 08:14:47
%S 2,180,2090880,6044699520000,7151106328088486400000,
%T 5159620144413185246982598164480000,
%U 3167269298042065159436486399933762922086400000000,2200712918907364598767850489247066133407004510957047455416320000000
%N a(n) = Product_{k=0..n} (n^2+k)^k.
%F a(n) = ((n^2+n)!)^(n+1) / A272238(n).
%F a(n) ~ exp(n/3 + 3/8) * n^(n*(n+1)).
%t Table[Product[(n^2+k)^k, {k, 0, n}], {n, 1, 10}]
%t Table[((n^2+n)!)^(n+1) * BarnesG[n^2 + 1] / BarnesG[n^2 + n + 2], {n, 1, 10}]
%Y Cf. A272163, A272180, A272238.
%K nonn,easy
%O 1,1
%A _Vaclav Kotesovec_, Apr 23 2016