%N Number of twice-crossing partitions on n nodes.
%C The meandric numbers A005316 are the numbers of paths which cross themselves 0 times.
%C This sequence is the number of paths that must cross themselves exactly twice.
%H B. W. J. Irwin, <a href="https://www.authorea.com/users/5445/articles/173040-on-the-number-of-k-crossing-partitions/_show_article">On the number of k-crossing partitions</a>
%e a(4) = 8; this is from the partitions
%e (2,1,4,3), (2,4,3,1),
%e (3,2,4,1), (3,4,2,1),
%e (4,1,3,2), (4,2,1,3),
%e (4,2,3,1), (4,3,1,2).
%Y Cf. A005316, A287220.
%A _Benedict W. J. Irwin_, May 22 2017