Is there a formula which gives the number of connected bipartite graphs with $n$ vertices such that the degree of every vertex is at most $d$? I can determine the results computationally using nauty, but it would be nice if there were a published formula I could use and cite instead.
Hanlon [1] gives formulas for determining the number of connected bipartite graphs by order, but not for capping the results to a maximum degree.
[1] Phil Hanlon. The enumeration of bipartite graphs. Discrete Mathematics 28, 1979, pp. 49–57.