# Counting non-nesting binary strings

A binary string $$S$$ of length $$2n$$ is said to be non-nesting if there is a perfect matching $$M$$ between identical bits such that no two edges of $$M$$ are nesting.

Edges (2, 4) and (1, 6) are nesting (integers represents the location of identical bits inside the string $$010110$$).

What is the number of non-nesting binary strings?

• Have you tried computing this for several small values of $n$, then seeing if the answer is in OEIS? – Mike Earnest Jan 20 at 22:41
• I only ask because I have no other idea how to proceed. – Mike Earnest Jan 20 at 22:52