OFFSET
5,1
COMMENTS
a(n) is the number of coalescent histories for matching gene tree G and species tree S, where G and S are identically labeled and have shape (...((((A_1,A_2),A_3),(A_4,A_5)),.),.),...), with n leaves.
LINKS
N. A. Rosenberg, Coalescent histories for caterpillar-like families, IEEE/ACM Trans. Comp. Biol. Bioinformat. 10 (2013), 1253-1262.
FORMULA
a(n) = ((23*n^2-131*n+180)/(4*(2n-3)*(2n-5)))*(2n-2)!/((n-1)!*n!).
a(n) = ((23*n^2-131*n+180)/(4*(2n-3)*(2n-5)))*A000108(n-1).
CROSSREFS
KEYWORD
nonn
AUTHOR
Noah A Rosenberg, Jun 16 2022
STATUS
approved