  Hickerson made an explicit formula for Dedekind sums $s(p,q)$ in terms of the
continued fraction of $p/q$. We develop analogous formula for generalized
Dedekind sums $s_{i,j}(p,q)$ defined in association with the
$x^{i}y^{j}$-coefficient of the Todd power series of the lattice cone in
$\Bbb{R}^2$ generated by $(1,0)$ and $(p,q)$. The formula generalizes
Hickerson's original one and reduces to Hickerson's for $i=j=1$. In the
formula, generalized Dedekind sums are divided into two parts: the integral
$s^I_{ij}(p,q)$ and the fractional $s^R_{ij}(p,q)$. We apply the formula to
Siegel's formula for partial zeta values at a negative integer and obtain a new
expression which involves only $s^I_{ij}(p,q)$ the integral part of generalized
Dedekind sums. This formula directly generalize Meyer's formula for the special
value at $0$. Using our formula, we present the table of the partial zeta value
at $s=-1$ and $-2$ in more explicit form. Finally, we present another
application on the equidistribution property of the fractional parts of the
graph $\Big{(}\frac{p}{q},R_{i+j}q^{i+j-2} s_{ij}(p,q)\Big{)}$ for a certain
integer $R_{i+j}$ depending on $i+j$.
