Observations on Motzkin numbers

[David Wilson]

A001006 is the Motzkin numbers, while A064189 is the Motzkin triangle.
We have A001006(n) = A064189(n, 0).  The two sequences should reference
one another.

Also, A001006 gives the number of ways of drawing any number of
nonintersecting chords between n points on a circle, while A054726 gives
the number of ways of drawing noncrossing chords between n points on a
circle.  The difference is that nonintersection chords have no point in
common, while noncrossing chords may share an endpoint.  I think A001006
and A064189 should reference one another.  Also, I was wondering if there
would be formulae for A001006 analogous to the many formulae for A001006,
especially the Motzkin triangle.