OFFSET
1,2
COMMENTS
Cardinality of the set of nesting-similarity classes.
Number of Lyngsø-Pedersen structures with n arcs [Saule et al., Theorem 1]. - Eric M. Schmidt, Sep 20 2017
LINKS
M. Klazar, On identities concerning the numbers of crossings and nestings of two edges in matchings, arXiv:math/0503012 [math.CO], 2005.
Cédric Saule, Mireille Regnier, Jean-Marc Steyaert, Alain Denise, Counting RNA pseudoknotted structures (extended abstract), dmtcs:2834 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
FORMULA
G.f.: C+z^2(2zC'+C)^2C, with C(z) the g.f. of the Catalan numbers.
G.f.: (x*(8*x+5*Sqrt[1-4 x]-9)-2*Sqrt[1-4 x]+2)/(2*(1-4*x)*x^2). [Harvey P. Dale, Oct 03 2011]
D-finite with recurrence 2*(n+1)*a(n) +(-21*n+1)*a(n-1) +2*(36*n-43)*a(n-2) +40*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jun 08 2016
MATHEMATICA
Table[2 4^(n-1)-(3n-1)/(2n+2) Binomial[2n, n], {n, 30}] (* Harvey P. Dale, Oct 03 2011 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Ralf Stephan, Apr 17 2005
STATUS
approved