OFFSET
0,4
COMMENTS
Column 0 of the triangle A101307.
LINKS
Emeric Deutsch, Ordered trees with prescribed root degrees, node degrees and branch lengths, Discrete Math., 282, 2004, 89-94.
J. Riordan, Enumeration of plane trees by branches and endpoints, J. Comb. Theory (A) 19, 1975, 214-222.
FORMULA
G.f.: [1-z^2+z^3-sqrt[(1-z^2+z^3)(1-4z+3z^2-3z^3)]]/[2z(1-z+z^2)].
D-finite with recurrence (n+2)*a(n) +(-5*n-4)*a(n-1) +(7*n+2)*a(n-2) +(-4*n-5)*a(n-3) +(-7*n+31)*a(n-4) +3*(5*n-22)*a(n-5) +2*(-8*n+41)*a(n-6) +9*(n-6)*a(n-7) +3*(-n+7)*a(n-8)=0. - R. J. Mathar, May 31 2014
EXAMPLE
a(3)=3 because we have:(i) a path of length tree hanging from the root, (ii) an edge hanging from the root, from the end of which two edges are hanging and (iii) three edges hanging from the root.
MAPLE
G:=(1-z^2+z^3-sqrt((1-z^2+z^3)*(1-4*z+3*z^2-3*z^3)))/2/z/(1-z+z^2): Gser:=series(G, z=0, 34): 1, seq(coeff(Gser, z^n), n=1..32);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 22 2004
STATUS
approved