On enumeration of labelled connected graphs by the number of cutpoints

We study the numbers $S_{mn}$ of labelled connected graphs with $n$ vertices among which $m$ are cutpoints. We obtain an explicit expression for the exponential generating function $S_m(z)$ of these numbers and find the asymptotics of the numbers $S_{mn}$ as $n\to\infty$ and $m=o(n)$.