OFFSET
0,6
COMMENTS
Or number of ordered trees with n edges, no vertices of outdegree 1 and which are symmetrical with respect to the vertical axis passing through the root.
LINKS
F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999), 73-112.
FORMULA
G.f.: [(1-z)(1+z^2)-(1+z)sqrt(1-2z^2-3z^4)]/[2z(z^3+z^2+z-1)].
D-finite with recurrence (n+1)*a(n) -2*a(n-1) +4*(-n+1)*a(n-2) +2*(-n+2)*a(n-3) +4*a(n-4) +2*(2*n-3)*a(n-5) +4*(2*n-11)*a(n-6) +6*(n-6)*a(n-7) +3*(n-7)*a(n-8)=0. - R. J. Mathar, Jul 24 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 26 2003
STATUS
approved