  In this short note, we compute the precise asymptotics for the number of
contingency tables with non-uniform margins. More precisely, for parameter
$n,\delta, B,C>0$, we consider the set of matrices whose first $[n^\delta]$
rows and columns have sum $[BCn]$ and the rest $n$ rows and columns have sum
$[Cn]$. We compute the precise asymptotics of the cardinality of this set when
$B<B_c=1+\sqrt{1+1/C}$ using the maximal entropy methods developed by Barvinok
and Hartigan. The only contribution of this note is a detailed expansion of the
determinant of quadratic forms in asymptotic formulas.
