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A293881
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Number T(n,k) of linear chord diagrams having n chords and minimal chord length k (or k=0 if n=0); triangle T(n,k), n>=0, 0<=k<=n, read by rows.
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16
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1, 0, 1, 0, 2, 1, 0, 10, 4, 1, 0, 69, 26, 9, 1, 0, 616, 230, 79, 19, 1, 0, 6740, 2509, 854, 252, 39, 1, 0, 87291, 32422, 11105, 3441, 796, 79, 1, 0, 1305710, 484180, 167273, 52938, 14296, 2468, 159, 1, 0, 22149226, 8203519, 2855096, 919077, 265103, 59520, 7564, 319, 1
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OFFSET
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0,5
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COMMENTS
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Conjecture: column k>0 is asymptotic to (exp(-k+1) - exp(-k)) * 2^(n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, Oct 25 2017
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LINKS
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EXAMPLE
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Triangle T(n,k) begins:
1;
0, 1;
0, 2, 1;
0, 10, 4, 1;
0, 69, 26, 9, 1;
0, 616, 230, 79, 19, 1;
0, 6740, 2509, 854, 252, 39, 1;
0, 87291, 32422, 11105, 3441, 796, 79, 1;
0, 1305710, 484180, 167273, 52938, 14296, 2468, 159, 1;
...
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CROSSREFS
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Columns k=0-10 give: A000007, A293914, A293915, A293916, A293917, A293918, A293919, A293920, A293921, A293922, A293923.
Main diagonal and first lower diagonal give: A000012, A054135 (for n>0).
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KEYWORD
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AUTHOR
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STATUS
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approved
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