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A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that no two vertices in the same set are adjacent.

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Enumeration of labeled connected bipartite graphs given partite sets

Found the answer in Labeled Bipartite Blocks by F. Harary and R. W. Robinson (http://cms.math.ca/cjm/v31/cjm1979v31.0060-0068.pdf , page 63, formula 11): $$C(m, n) = 2^{nm} - \sum{* \binom{n - 1}{a - …
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Enumeration of labeled connected bipartite graphs given partite sets

What would be the closed-form expression defining number of all possible labelled connected bipartite graphs given $\mid X \mid = m, \mid Y \mid = n - m $?