OFFSET
0,2
FORMULA
a(n) = Product_{k=0..n} binomial(4*k,k) * binomial(3*k,k) * binomial(2*k,k).
a(n) ~ A^(15/4) * sqrt(Gamma(1/4)) * 2^(4*n^2 + 7*n/2 - 7/6) * exp(3*n/2 - 5/16) / (n^(3*n/2 + 17/16) * Pi^(3*n/2 + 7/4)), where A is the Glaisher-Kinkelin constant A074962.
MATHEMATICA
Table[Product[(4*k)!/k!^4, {k, 0, n}], {n, 0, 10}]
Table[Product[Binomial[4*k, k] * 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