Let $K(m,n)$ denotes the complete bipartite graph on parts of cardinality $m$ and $n$.

My question is; How many nonisomorphic spanning subgraphs are there of of $K(m,n)$? This is such an obvious question, it has probably been answered. I just don't know where to look. There is an obvious, but complex to use, recursion for the constructions. Given the set of nonisomorphic subgraphs of $K(m-1,n)$ -- or of $K(m,n-1)$ -- appending the $n-1$ edges from the missing vertex in the first case or $m-1$ in the second edges in all inequivalent ways will generate the set for $K(m,n)$. But this is not a numerical problem so no simple recursion seems possible -- yet it may have well been solved using Polya's counting theorem. Do any of you know the answer, or where it can be found?