OFFSET
0,2
COMMENTS
Generally, for p > 1 is
binomial(p*n,n) ~ (p^p/(p-1)^(p-1))^n * sqrt(p/(2*Pi*n*(p-1))) * (1 - (p^2-p+1)/(12*n*p*(p-1))).
binomial(p*n,n)^n ~ exp(-(p^2-p+1)/(12*p*(p-1))) * (p^p/(p-1)^(p-1))^(n^2) * (p/(2*Pi*n*(p-1)))^(n/2).
FORMULA
a(n) ~ exp(-7/72) * 3^(3*n^2 + n/2) / (2^(2*n^2 + n) * Pi^(n/2) * n^(n/2)).
MATHEMATICA
Table[Binomial[3n, n]^n, {n, 0, 10}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 26 2015
STATUS
approved