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

Author

Alois P. Heinz, Oct 20 2017

Keywords

• nonn
• tabl

Comments

All terms in columns k > 1 are even.

Examples

			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;
  ...
		

Links

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

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.

Formula

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