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A293881
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.
16
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
OFFSET
0,5
COMMENTS
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
EXAMPLE
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;
...
CROSSREFS
Row sums give A001147.
T(2n,n) gives A290688.
Main diagonal and first lower diagonal give: A000012, A054135 (for n>0).
Sequence in context: A021478 A115563 A364068 * A362308 A185285 A268434
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Oct 18 2017
STATUS
approved