In [11], Hickerson made an explicit formula for Dedekind sums 2314X16301548&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=a793f7facdb680f1d93c110e62574a92" title="Click to view the MathML source">s(p,q) in terms of the continued fraction of 2314X16301548&_mathId=si2.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=c754417fa40160ef3561c82ad5e61478" title="Click to view the MathML source">p/q. We develop analogous formula for generalized Dedekind sums 2314X16301548&_mathId=si3.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=50921a92e992d9bcb46d77112310dc01" title="Click to view the MathML source">si,j(p,q) defined in association with the 2314X16301548&_mathId=si4.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=6d8bba80a3ff6f6fa5cbf0fd6f7131e9" title="Click to view the MathML source">xiyj-coefficient of the Todd power series of the lattice cone in 2314X16301548&_mathId=si5.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=a6e0cd47c5e9badb8a166515fc840d6b" title="Click to view the MathML source">R2 generated by 2314X16301548&_mathId=si6.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=92f11dee46d081ca88d5b5d14cd7c151" title="Click to view the MathML source">(1,0) and 2314X16301548&_mathId=si7.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=3481483978028da6fd62d31f9d298748" title="Click to view the MathML source">(p,q). The formula generalizes Hickerson's original one and reduces to Hickerson's for 2314X16301548&_mathId=si8.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=956405bad31eb5d3a361ec5075979e01" title="Click to view the MathML source">i=j=1. In the formula, generalized Dedekind sums are divided into two parts: the integral 2314X16301548&_mathId=si9.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=099c6f0e102a6cedc9ffbf32a46641bb">2314X16301548-si9.gif"> and the fractional 2314X16301548&_mathId=si10.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=d90ac1223f8bb67d181b25c20727c386">2314X16301548-si10.gif">. We apply the formula to Siegel's formula for partial zeta values at a negative integer and obtain a new expression which involves only 2314X16301548&_mathId=si9.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=099c6f0e102a6cedc9ffbf32a46641bb">2314X16301548-si9.gif"> the integral part of generalized Dedekind sums. This formula directly generalizes Meyer's formula for the special value at 0. Using our formula, we present the table of the partial zeta value at 2314X16301548&_mathId=si11.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=689ff79aa1b80b4bb5d1d0ad78b952b6" title="Click to view the MathML source">s=−1 and −2 in more explicit form. Finally, we present another application on the equidistribution property of the fractional parts of the graph 2314X16301548&_mathId=si12.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=02df000922d3a943c32a4fa5535f840f">2314X16301548-si12.gif"> for a certain integer 2314X16301548&_mathId=si13.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=285c25c2919bc817ce00b24b2077146a" title="Click to view the MathML source">Ri+j depending on 2314X16301548&_mathId=si14.gif&_user=111111111&_pii=S0022314X16301548&_rdoc=1&_issn=0022314X&md5=feebb1991c9eb9545515f1bc4b33537f" title="Click to view the MathML source">i+j.