Pseudogamy is a form of asexual reproduction since there is no union of gametes involved. It may be in the form of parthenogenesis wherein the sperm stimulates the egg cell to form an embryo without the need to fertilize it. In this way there are no genes from the male that are inherited. This is also referred to as gynogenesis.1 In this form of reproduction, mating is still required so that the sperm would stimulate the egg cell although no genetic material will be contributed during the development of an offspring. This is seen in certain salamanders of the genus Ambystoma.
In a restrictive sense, pseudogamy may also pertain to a reproductive process where in plants the embryo develops from the fusion of vegetative cells rather than of gametes. This is exemplified by the so-called pseudogamous apomixis as seen in Rosaceae and Poaceae, e.g. the Himalayan blackberry Rubus armeniacus and gamagrass Tripsacum dactyloides. In this mode of reproduction, pollination is required but there is no male inheritance.
1 Engelstädter, J. (2008). Constraints on the evolution of asexual reproduction. BioEssays. Review Article. 30(11–12): 1138–1150.