  We study the asymptotic expansion of the colored Jones polynomial (the
Melvin-Morton expansion) using a recursion formula for the deframed universal
weight system for the $sl(2)$ Lie algebra. Combined with the formula for the
universal weight system for the Lie superalgebra $gl(1|1)$ (which corresponds
to the Alexander-Conway knot polynomial) this formula gives a very short proof
of the Melvin-Morton conjecture relating the colored Jones invariant and the
Alexander-Conway polynomial of knots.
