Motzkin number

Motzkin number
Named after	Theodore Motzkin
Publication year	1948
Author of publication	Theodore Motzkin
No. of known terms	infinity
Formula	see Properties
First terms	1, 1, 2, 4, 9, 21, 51
OEIS index	A001006; Motzkin;

In mathematics, the $n$ th Motzkin number is the number of different ways of drawing non-intersecting chords between $n$ points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have diverse applications in geometry, combinatorics and number theory.

The Motzkin numbers $M_{n}$ for $n=0,1,\dots$ form the sequence:

1, 1, 2, 4, 9, 21, 51, 127, 323, 835, ... (sequence A001006 in the OEIS)