[seqfan] unlabeled Motzkin numbers

[Max Alekseyev]

Just out of curiosity, what would be an "unlabeled" version of Motzkin
numbers A001006?
That is, number of ways of drawing any number of nonintersecting
chords joining n unlabeled equally spaced points on a circle (in other
words, the points and chords are distinguished up to rotations of the
circle).
Is this sequence in the OEIS?

Furthermore, is there a variant of counting up to rotations and
reflections of the circle?

Regards,
Max