A293157 Triangle read by rows: T(n,k) = number of linear chord diagrams with n chords such that every chord has length at least k (1 <= k <= n).

1, 3, 1, 15, 5, 1, 105, 36, 10, 1, 945, 329, 99, 20, 1, 10395, 3655, 1146, 292, 40, 1, 135135, 47844, 15422, 4317, 876, 80, 1, 2027025, 721315, 237135, 69862, 16924, 2628, 160, 1, 34459425, 12310199, 4106680, 1251584, 332507, 67404, 7884, 320, 1, 654729075, 234615096, 79154927, 24728326, 6944594, 1627252, 269616, 23652, 640, 1

Offset

1,2

Comments

There is a surprising change in notation in Sullivan (2016) between Definition 1 and Table 1.

The first 11 columns are given in the reference.

Links

Table of n, a(n) for n=1..55.

Everett Sullivan, Linear chord diagrams with long chords, arXiv preprint arXiv:1611.02771 [math.CO], 2016.

Example

Triangle begins:
      1;
      3,    1;
     15,    5,    1;
    105,   36,   10,    1;
    945,  329,   99,   20,    1;
  10395, 3655, 1146,  292,   40,    1;
  ...

Crossrefs

Cf. A000806, A001147, A190823, A190824, A190825, A020714, A278990, A293156, A293881.

Sequence in context: A269950 A190088 A119301 * A121335 A126454 A293558

Adjacent sequences: A293154 A293155 A293156 * A293158 A293159 A293160

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 10 2017

Extensions

More terms from Alois P. Heinz, Oct 17 2017

Status

approved