  We formulate a conjecture (already proven by A. Kricker) about the structure
of Kontsevich integral of a knot. We describe its value in terms of the
generating functions for the numbers of external edges attached to closed
3-valent diagrams. We conjecture that these functions are rational functions of
the exponentials of their arguments, their denominators being the powers of the
Alexander-Conway polynomial. This conjecture implies the existence of an
expansion of a colored Jones (HOMFLY) polynomial in powers of q-1 whose
coefficients are rational functions of q^color. We show how to derive the first
Kontsevich integral polynomial associated to the theta-graph from the rational
expansion of the colored SU(3) Jones polynomial.
