A371646 - OEIS

%I #9 Apr 29 2024 07:58:56

%S 1,1,8,59942025,239830737497318918172122578944,

%T 788243862228623056807478850630904903414781894638966172447366478063616699218750

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

%F 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 Table[Product[Binomial[n^3, k^3], {k, 0, n}], {n, 0, 6}]

%Y Cf. A001142, A371603.

%Y Cf. A007685, A255358, A371468.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 31 2024