OFFSET
0,2
FORMULA
a(n) = Product_{k=0..n} binomial(3*k,k) * binomial(2*k,k).
a(n) ~ A^(8/3) * Gamma(1/3)^(1/3) * 3^(3*n^2/2 + 2*n + 11/36) * exp(n - 2/9) / (n^(n + 13/18) * (2*Pi)^(n + 7/6)), where A is the Glaisher-Kinkelin constant A074962.
MATHEMATICA
Table[Product[(3*k)!/k!^3, {k, 0, n}], {n, 0, 10}]
Table[Product[Binomial[3*k, k] * Binomial[2*k, k], {k, 0, n}], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 23 2023
STATUS
approved