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A371646
a(n) = Product_{k=0..n} binomial(n^3, k^3).
2
1, 1, 8, 59942025, 239830737497318918172122578944, 788243862228623056807478850630904903414781894638966172447366478063616699218750
OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 31 2024
STATUS
approved