%I #5 Apr 20 2016 17:08:23

%S 1,1,48,1567641600,9698137182219213471744000000,

%T 21488900044302744250061179567064173417691432878080000000000000000

%N a(n) = Product_{k=0..n} (k*n)!.

%C The next term has 126 digits.

%F a(n) ~ A^n * n^(1/4 + 13*n/12 + n^2 + n^3) * (2*Pi)^(1/4 + n/2) / exp(n*(2 + 2*n + 3*n^2)/4), where A = A074962 is the Glaisher-Kinkelin constant.

%t Table[Product[(k*n)!, {k, 0, n}], {n, 0, 6}]

%Y Cf. A000178, A098694, A268504, A268505, A268506, A271946.

%Y Cf. A255322, A272093.

%K nonn,easy

%O 0,3

%A _Vaclav Kotesovec_, Apr 20 2016