  We give formulas expressing Milnor invariants of an n-component link L in the
3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor
invariant \bar{\mu}_J(L) vanishes for any sequence J with length at most k,
then any Milnor \bar{\mu}-invariant \bar{\mu}_I(L) with length between 3 and
2k+1 can be represented as a combination of HOMFLYPT polynomial of knots
obtained from the link by certain band sum operations. In particular, the
`first non vanishing' Milnor invariants can be always represented as such a
linear combination.
