A293961 Number T(n,k) of linear chord diagrams having n chords and maximal 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, 1, 2, 0, 1, 4, 10, 0, 1, 10, 24, 70, 0, 1, 20, 82, 212, 630, 0, 1, 42, 300, 798, 2324, 6930, 0, 1, 84, 894, 3800, 10078, 30188, 90090, 0, 1, 170, 2744, 18186, 51804, 150046, 452724, 1351350, 0, 1, 340, 8594, 71624, 313006, 851692, 2545390, 7695828, 22972950

Offset

0,6

Comments

All terms in columns k > 1 are even.

Links

Alois P. Heinz, Rows n = 0..20, flattened

Formula

A(n,k) = A293960(n,k) - A293960(n,k-1) for k>0, A(n,0) = A000007(n).

Example

Triangle T(n,k) begins:
  1;
  0, 1;
  0, 1,   2;
  0, 1,   4,   10;
  0, 1,  10,   24,    70;
  0, 1,  20,   82,   212,   630;
  0, 1,  42,  300,   798,  2324,   6930;
  0, 1,  84,  894,  3800, 10078,  30188,  90090;
  0, 1, 170, 2744, 18186, 51804, 150046, 452724, 1351350;
  ...

Crossrefs

Columns k=0-2 give: A000007, A057427, A167030(n+1).

Row sums give A001147.

Main diagonal gives A293962.

T(2n,n) gives A293963.

Cf. A293881, A293960.

Sequence in context: A244128 A016584 A378237 * A378239 A378238 A378240

Adjacent sequences: A293958 A293959 A293960 * A293962 A293963 A293964

Keyword

nonn,tabl

Author

Alois P. Heinz, Oct 20 2017

Status

approved