Let be the number of interlacing chords joining points on the circle. Let . Then . This formula was conjectured by J. Betramas. The number is also the number of interlacing involutions of points on the real line.

Permutations, words, matrices (msc 05A05), Exact enumeration problems, generating functions (msc 05A15)
CWI
Department of Analysis, Algebra and Geometry [AM]

Hazewinkel, M, & Kalashnikov, V.V. (1995). Counting interlacing pairs on the circle. Department of Analysis, Algebra and Geometry [AM]. CWI.