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A125660 Number of 3-noncrossing tangled-diagrams. 0
2, 7, 39, 292, 2635, 27019, 304162, 3677313 (list; graph; refs; listen; history; text; internal format)
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.

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: A330470 A266310 A032118 * 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

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Last modified June 16 15:37 EDT 2021. Contains 345063 sequences. (Running on oeis4.)