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 A082989 Number of ordered trees with n edges and having no root-to-leaf branches. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 30 12:38 EST 2023. Contains 367461 sequences. (Running on oeis4.)