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

0,13

Comments

All terms in columns k > 0 are odd.

Links

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

Formula

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

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

Example

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, ...

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.

Sequence in context: A355692 A192003 A226873 * A062719 A305161 A250484

Adjacent sequences: A293957 A293958 A293959 * A293961 A293962 A293963

Keyword

nonn,tabl

Author

Alois P. Heinz, Oct 20 2017

Status

approved