[seqfan] Q: unlabeled 2-regular digraphs

[Richard J. Mathar]

A007107 counts the labeled 2-regular digraphs with n nodes;
in A007108 we have the connected ones, in A001499 admitting loops.
Does the OEIS show somewhere the graphs without node labels, I mean the 
digraphs where indegree=outdegree=2?

The natural variants of such a sequence would be: 
 2-regular digraphs connected, loopless
 2-regular digraphs, loopless, not necessarily connected
 2-regular digraphs connected, loops allowed
 2-regular digraphs, loops allowed, not necessarily connected