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%I #4 Apr 21 2016 16:49:06
%S 1,1,2,1440,689762304000,1678124094566146045378560000000,
%T 445127215203413988036981576746329306509322538188800000000000000
%N a(n) = Product_{k=0..n} (k^2-k)!.
%C The next term has 114 digits.
%F a(n) ~ c * n^(n*(2*n^2 + 1)/3) * (2*Pi)^(n/2) / exp(5*n^3/9 + n/2 - Zeta(3) / (2*Pi^2)), where c = Product_{k>=2} (k*(k-1))!/stirling(k*(k-1)) = 1.086533635964823338078329042... and stirling(n) = sqrt(2*Pi*n) * n^n / exp(n) is the Stirling approximation of n!.
%t Table[Product[(k^2-k)!, {k, 0, n}], {n, 0, 8}]
%Y Cf. A272094, A272167.
%K nonn,easy
%O 0,3
%A _Vaclav Kotesovec_, Apr 21 2016
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