A082989 Number of ordered trees with n edges and having no root-to-leaf branches.

1, 0, 0, 1, 4, 13, 42, 139, 470, 1616, 5632, 19852, 70654, 253559, 916558, 3334211, 12197142, 44842184, 165597008, 613991206, 2284809072, 8530458154, 31945128628, 119960276246, 451621453764, 1704240175868, 6445111657272

Offset: 0

Author

Emeric Deutsch, May 29 2003

Keywords

• nonn

Formula

a(n) = 2*sum((-1)^j*(j+2)*C(2n-3-2j,n), j=0..floor((n-3)/2))/(n+1).

G.f.: 2(1-z)/[1+z+(1-z)sqrt(1-4z)].

D-finite with recurrence +2*(n+1)*a(n) +6*(-2*n+1)*a(n-1) +(19*n-35)*a(n-2) +(-13*n+32)*a(n-3) +2*(2*n-7)*a(n-4)=0. - R. J. Mathar, Jul 26 2022