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A080159
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Triangular array of ways of drawing k non-intersecting chords between n points on a circle; i.e. Motzkin polynomial coefficients.
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3
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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FORMULA
| For n>=2k: T(n, k) = n!/((n-2k)!k!(k+1)!) =A007318(n, 2k)*A000108(k).
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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.
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CROSSREFS
| Visible version of A055151. Row sums are A001006 (Motzkin numbers). Columns include A000012, A000217, A034827 and perhaps A000910.
Sequence in context: A126723 A090030 A202023 * A144299 A060514 A176788
Adjacent sequences: A080156 A080157 A080158 * A080160 A080161 A080162
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jan 31 2003
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