%I #20 Jan 26 2024 09:50:24

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

%N Number of 3-noncrossing tangled-diagrams.

%H William Y. C. Chen, Jing Qin and Christian M. Reidys, <a href="https://arxiv.org/abs/0710.4053">Crossings and nesting in tangled-diagrams</a>, arXiv:0710.4053 [math.CO], 2007.

%F 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]

%K nonn,more

%O 1,1

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