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

1, 1, 8, 59942025, 239830737497318918172122578944, 788243862228623056807478850630904903414781894638966172447366478063616699218750

Offset

0,3

Links

Table of n, a(n) for n=0..5.

Formula

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.

Mathematica

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

Crossrefs

Cf. A001142, A371603.

Cf. A007685, A255358, A371468.

Sequence in context: A076916 A076917 A076923 * A076911 A182010 A051269

Adjacent sequences: A371643 A371644 A371645 * A371647 A371648 A371649

Keyword

nonn

Author

Vaclav Kotesovec, Mar 31 2024

Status

approved