%I #12 Apr 25 2024 08:20:37
%S 1,1,40320,439039216240867959122165760000000
%N Product_{k=0..n} (k^3)!.
%C The next term a(4) has 122 digits.
%H Vaclav Kotesovec, <a href="/A255358/b255358.txt">Table of n, a(n) for n = 0..6</a>
%F a(n) ~ c * n^(29/40 + 3*n/2 + 3*n^2/4 + 3*n^3/2 + 3*n^4/4) * (2*Pi)^(n/2) / exp(n*(n+2)*(12 - 6*n + 7*n^2)/16), where c = A255511 = 4.113740552015338123052453340090368136...
%F a(n) = Product_{j=1..n^3} j^(n - ceiling(j^(1/3)) + 1). - _Vaclav Kotesovec_, Apr 25 2024
%t Table[Product[(k^3)!, {k, 0, n}], {n, 0, 6}]
%t Table[Product[j^(n - Ceiling[j^(1/3)] + 1), {j, 1, n^3}], {n, 0, 6}] (* _Vaclav Kotesovec_, Apr 25 2024 *)
%Y Cf. A000178, A255322, A255359, A255360.
%Y Cf. A002109, A051675, A255321, A255323, A255344.
%Y Cf. A000142, A255268, A255269, A255511.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Feb 21 2015