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

Author

Alois P. Heinz, Oct 18 2017

Keywords

• nonn
• tabl

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

Examples

			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

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.