  This paper is devoted to the evaluation of the generating series of the
connection coefficients of the double cosets of the hyperoctahedral group.
Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a
partition $\nu$, gives the spectral distribution of some random real matrices
that are of interest in random matrix theory. We provide an explicit evaluation
of this series when $\nu=(n)$ in terms of monomial symmetric functions. Our
development relies on an interpretation of the connection coefficients in terms
of locally orientable hypermaps and a new bijective construction between
locally orientable partitioned hypermaps and some permuted forests.
