A080159 Triangular array of ways of drawing k non-intersecting chords between n points on a circle; i.e., Motzkin polynomial coefficients.

1, 1, 0, 1, 1, 0, 1, 3, 0, 0, 1, 6, 2, 0, 0, 1, 10, 10, 0, 0, 0, 1, 15, 30, 5, 0, 0, 0, 1, 21, 70, 35, 0, 0, 0, 0, 1, 28, 140, 140, 14, 0, 0, 0, 0, 1, 36, 252, 420, 126, 0, 0, 0, 0, 0, 1, 45, 420, 1050, 630, 42, 0, 0, 0, 0, 0, 1, 55, 660, 2310, 2310, 462, 0, 0, 0, 0, 0, 0, 1, 66, 990, 4620

Offset: 0

Author

Henry Bottomley, Jan 31 2003

Keywords

• nonn
• tabl

Examples

			Rows start: 1; 1,0; 1,1,0; 1,3,0,0; 1,6,2,0,0; 1,10,10,0,0,0; 1,15,30,5,0,0,0; etc.
		

Crossrefs

Visible version of A055151. Row sums are A001006 (Motzkin numbers). Columns include A000012, A000217, A034827 and perhaps A000910.

Formula

For n >= 2k: T(n, k) = n!/((n-2k)!k!(k+1)!) = A007318(n, 2k)*A000108(k).

T(n,k) = A055151(n,k).