These numbers are catalan numbers:
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452
F(0) = 1
F(1) = 1
F(2) = 2
F(3) = 5
F(4) = 14
….
The formula of catalan could be:
Some cases of catalan numbers are below:
:
Actually, the dyck word and parentheses groups are the same of stack in-out sequence.
Focus on a certain point, try to draw a chord from a that point, which can divide rest of the points into 2 even parts.