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

0,8

Links

Table of n, a(n) for n=0..81.

Formula

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

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

Example

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.

Sequence in context: A293616 A211649 A202023 * A144299 A060514 A176788

Adjacent sequences: A080156 A080157 A080158 * A080160 A080161 A080162

Keyword

nonn,tabl

Author

Henry Bottomley, Jan 31 2003

Status

approved