log[(C[3n,n]/C[2n,n])^{1/n}]
=(1/n)log(C[3n,n]/C[2n,n])
=(1/n)log({3n(3n-1)…(2n+1)2n}/{2n(2n-1)…(n+1)n})
=(1/n)log({(3n)/(2n)}{(3n-1)/(2n-1)}…{(2n)/n)})
=…