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A371646 a(n) = Product_{k=0..n} binomial(n^3, k^3).

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%I A371646 #9 Apr 29 2024 07:58:56
%S A371646 1,1,8,59942025,239830737497318918172122578944,
%T A371646 788243862228623056807478850630904903414781894638966172447366478063616699218750
%N A371646 a(n) = Product_{k=0..n} binomial(n^3, k^3).
%F A371646 a(n) ~ c * exp((9/4 - sqrt(3)*Pi/8)*n^4 + (3*zeta(3)/(4*Pi^2) - Pi/(4*sqrt(3)) + 3)*n) / ((2*Pi)^(n/2) * A^(3*n^2) * 3^(9*n^4/8 - n^2/4 + 3*n/4) * n^(n^2/4 + 3*n/2 - 8/15)), where c = 0.498332919... and A is the Glaisher-Kinkelin constant A074962.
%t A371646 Table[Product[Binomial[n^3, k^3], {k, 0, n}], {n, 0, 6}]
%Y A371646 Cf. A001142, A371603.
%Y A371646 Cf. A007685, A255358, A371468.
%K A371646 nonn
%O A371646 0,3
%A A371646 _Vaclav Kotesovec_, Mar 31 2024