OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..380 (first 100 terms from Marko Riedel)
Marko Riedel, Even outdegree nodes among all labeled trees on n nodes
FORMULA
E.g.f.: (T^2+z^2)/(2*T*(1-T)) where T is the labeled tree function defined by T = z exp T.
EXAMPLE
When n=3 there are two types of trees: rooted paths on three nodes which have one even degree node (the bottom one with zero children), giving 6*1, and trees consisting of a node with two children, of which there are 3, and they have 3 even degree nodes, giving 3*3 for a total of 6*1 + 3*3 = 15.
MAPLE
a:= n-> n!*coeff(series((T->(T^2+x^2)/
(2*T*(1-T)))(-LambertW(-x)), x, n+2), x, n):
seq(a(n), n=1..30); # Alois P. Heinz, Jan 03 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Marko Riedel, Jan 03 2015
STATUS
approved