A293960 Number A(n,k) of linear chord diagrams having n chords and no chord length larger than k; square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 3, 1, 0, 1, 1, 3, 5, 1, 0, 1, 1, 3, 15, 11, 1, 0, 1, 1, 3, 15, 35, 21, 1, 0, 1, 1, 3, 15, 105, 103, 43, 1, 0, 1, 1, 3, 15, 105, 315, 343, 85, 1, 0, 1, 1, 3, 15, 105, 945, 1141, 979, 171, 1, 0, 1, 1, 3, 15, 105, 945, 3465, 4779, 2915, 341, 1, 0

Offset: 0

Author

Alois P. Heinz, Oct 20 2017

Keywords

• nonn
• tabl

Comments

All terms in columns k > 0 are odd.

Examples

			Square array A(n,k) begins:
  1, 1,  1,   1,    1,     1,     1,      1, ...
  0, 1,  1,   1,    1,     1,     1,      1, ...
  0, 1,  3,   3,    3,     3,     3,      3, ...
  0, 1,  5,  15,   15,    15,    15,     15, ...
  0, 1, 11,  35,  105,   105,   105,    105, ...
  0, 1, 21, 103,  315,   945,   945,    945, ...
  0, 1, 43, 343, 1141,  3465, 10395,  10395, ...
  0, 1, 85, 979, 4779, 14857, 45045, 135135, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 0..40, flattened

Crossrefs

Columns k=0-10 give: A000007, A000012, A001045(n+1), A293995, A293996, A293997, A293998, A293999, A294000, A294001, A294002.

Main diagonal gives A001147.

Cf. A293961.

Formula

A(n,k) = Sum_{j=0..k} A293961(n,j).

A(n,k) = A(n,n) = A001147(n) for k >= n.