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

0,5

Links

Table of n, a(n) for n=0..26.

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

Crossrefs

Sequence in context: A010900 A175005 A070031 * A267240 A192802 A149425

Adjacent sequences: A082986 A082987 A082988 * A082990 A082991 A082992

Keyword

nonn

Author

Emeric Deutsch, May 29 2003

Status

approved