A125660 Number of 3-noncrossing tangled-diagrams.

2, 7, 39, 292, 2635, 27019, 304162, 3677313

Offset

1,1

Links

Table of n, a(n) for n=1..8.

William Y. C. Chen, Jing Qin and Christian M. Reidys, Crossings and nesting in tangled-diagrams, arXiv:0710.4053 [math.CO], 2007.

Formula

D_{2,k}(n) = Sum_{i=0..n} binomial(n,i) * T_{2,k} (n-i), where T_{2,k}(n) = Sum_{L=0..n} binomial(n,L) * f_k(2n-L), and f_k(2n-L) is the number of k-noncrossing matchings over 2n-L vertices. [edited, using formulas from p. 12 of the paper by Chen et al., by Jon E. Schoenfield, Jul 21 2019]

Crossrefs

Sequence in context: A266310 A032118 A369087 * A112944 A060073 A322152

Adjacent sequences: A125657 A125658 A125659 * A125661 A125662 A125663

Keyword

nonn,more

Author

Jing Qin (qj(AT)cfc.nankai.edu.cn), Oct 26 2007

Status

approved