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

0,5

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

Links

Table of n, a(n) for n=0..54.

Example

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.

Sequence in context: A021478 A115563 A364068 * A362308 A185285 A268434

Adjacent sequences: A293878 A293879 A293880 * A293882 A293883 A293884

Keyword

nonn,tabl

Author

Alois P. Heinz, Oct 18 2017

Status

approved