In 1996 Goulden and Jackson introduced a family of coefficients $( c_{π, σ}^λ ) $ indexed by triples of partitions which arise in the power sum expansion of some Cauchy sum for Jack symmetric functions $( J^{(α)}_π)$. The coefficients $ c_{π, σ}^λ $ can be viewed as an interpolation between the structure constants of the class algebra and the double coset algebra. Goulden and Jackson suggested that the coefficients $ c_{π, σ}^λ $ are polynomials in the variable $β:= α-1$ with non-negative integer coefficients and that there is a combinatorics of matching hidden behind them. This \emph{Matchings-Jack Conjecture} remains open. Doł\oldk{e}ga and Féray showed the polynomiality of connection coefficients $c^λ_{π,σ}$ and gave the upper bound on the degrees. We give a necessary and sufficient condition for the polynomial $ c_{π, σ}^λ$ to achieve this bound. We show that the leading coefficient of $ c_{π, σ}^λ$ is a positive integer and we present it in the context of Matchings-Jack Conjecture of Goulden and Jackson.