OFFSET
1,1
LINKS
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
KEYWORD
nonn,more
AUTHOR
Jing Qin (qj(AT)cfc.nankai.edu.cn), Oct 26 2007
STATUS
approved