# Number of connected subgraphs of the complete unlabelled graph

Is there an explicit formula for the number of connected graphs with at most $n$ vertices?

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Unless I've misunderstood you, just just want to know how many distinct connected graphs there are on $n$ vertices. There is nothing simple known. OEIS gives values for up to $K_{20}$ and some links to references.
It could be that OP wants the number of distinct connected graphs on at most $n$ vertices. Of course, your answer is still apropos. –  Gerry Myerson Jul 11 '12 at 5:24
Is there an explict formula for the number of connected graphs with at most $n$ vertics? –  Croq Jul 14 '12 at 21:28