A355044 Number of coalescent histories for matching gene trees and species trees with n leaves and a 5-leaf seed tree.

10, 37, 130, 453, 1584, 5577, 19786, 70720, 254524, 921842, 3357908, 12294995, 45229500, 167093505, 619689690, 2306312580, 8611143420, 32246815350, 121085968380, 455817192090, 1719872196432, 6503354706762, 24640476660420, 93534587913648, 355675196682904

Offset: 5

Author

Noah A Rosenberg, Jun 16 2022

Keywords

• nonn

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.

Crossrefs

Cf. A000108, A070031 (for the same computation with a 4-leaf seed tree).

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).