We find asymptotic formulas as $n\to\infty$ for the coefficients
$a(r\hbox{,}\,n)$ defined by
\abovedisplayskip2pt plus 2pt
\belowdisplayskip2pt plus 2pt
\def\nnu{{\hbox{\mathversion{normal}$\scriptstyle\nu$}}}
$$
\prod_{\nnu=1}^\infty\,(1-x^\nnu)^{-\nnu^r}
=\sum_{n=0}^\infty a(r\hbox{,}\,n)x^n\hbox{.}
$$
(The case $r=1$ gives the number of plane partitions of $n$.)
Generalized Dedekind sums occur naturally and are studied using the
Finite Fourier Transform. The methods used are unorthodox; many of
the computations are not justified but the result is in many cases
very good numerically. The last section gives various formulas for
Kinkelin's constant.