  We study relations between the Alexander-Conway polynomial $\nabla_L$ and
Milnor higher linking numbers of links from the point of view of finite-type
(Vassiliev) invariants. We give a formula for the first non-vanishing
coefficient of $\nabla_L$ of an m-component link L all of whose Milnor numbers
$\mu_{i_1... i_p}$ vanish for $p\le n$. We express this coefficient as a
polynomial in Milnor numbers of L. Depending on whether the parity of n is odd
or even, the terms in this polynomial correspond either to spanning trees in
certain graphs or to decompositions of certain 3-graphs into pairs of spanning
trees. Our results complement determinantal formulas of Traldi and Levine
obtained by geometric methods.
