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We find a Thron-type continued fraction (T-fraction) for the ordinarygenerating function of the Ward polynomials, as well as for somegeneralizations employing a large (indeed infinite) family of independentindeterminates. Our proof is based on a bijection between super-augmentedperfect matchings and labeled Schr\"oder paths, which generalizes Flajolet'sbijection between perfect matchings and labeled Dyck paths.

Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials