The number $\mathrm{con}_n$ counts partitions $X$ of $\{1,2,\ldots,2n\}$ into
$n$ two-element blocks such that the crossing graph of $X$ is connected.
Similarly, $\mathrm{cro}_n$ counts partitions whose crossing graph has
no isolated vertex. (If it has no edge, Catalan numbers arise.) We prove,
using a more generally aplicable criterion, that the sequences $(\mathrm{con}_n)$ and $(\mathrm{cro}_n)$ are not P-recursive. They are
even more ugly. On the other hand, we show that the residues
of $\mathrm{con}_n$ and $\mathrm{cro}_n$ modulo any given power of 2 can be
determined P-recursively. We consider also numbers $\mathrm{sco}_n$ of
symmetric connected partitions. Unfortunately, their OGF satisfies a more
complicated differential equation which we cannot handle.
