A080159 - OEIS

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

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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.