A293920 -id:A293920 - cp's OEIS frontend

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.

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

Alois P. Heinz, Oct 18 2017

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

			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;
  ...

Columns k=0-10 give: A000007, A293914, A293915, A293916, A293917, A293918, A293919, A293920, A293921, A293922, A293923.
Row sums give A001147.
T(2n,n) gives A290688.
Main diagonal and first lower diagonal give: A000012, A054135 (for n>0).
Cf. A293157, A293961.

cp's OEIS Frontend

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.

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