A power series is introduced that is an extension to three sets of variables of the Cauchy sum for Jack symmetric functions in the Jack parameter
α
.
\alpha .
We conjecture that the coefficients of this series with respect to the power sum basis are nonnegative integer polynomials in
b
b
, the Jack parameter shifted by
1
1
. More strongly, we make the Matchings-Jack Conjecture, that the coefficients are counting series in
b
b
for matchings with respect to a parameter of nonbipartiteness. Evidence is presented for these conjectures and they are proved for two infinite families. The coefficients of a second series, essentially the logarithm of the first, specialize at values
1
1
and
2
2
of the Jack parameter to the numbers of hypermaps in orientable and locally orientable surfaces, respectively. We conjecture that these coefficients are also nonnegative integer polynomials in
b
b
, and we make the Hypermap-Jack Conjecture, that the coefficients are counting series in
b
b
for hypermaps in locally orientable surfaces with respect to a parameter of nonorientability.