A253571 Total number of even outdegree nodes among all labeled rooted trees on n nodes.

1, 2, 15, 144, 1765, 26400, 466459, 9508352, 219651849, 5671088640, 161833149511, 5058050224128, 171837337744813, 6304955850432512, 248477268083174355, 10467916801317273600, 469451601966727952401, 22329535184262444220416, 1122809130124800181976575

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

Cf. A000169, A026641, A000081.

Sequence in context: A219868 A224885 A371575 * A111686 A371582 A001854

Adjacent sequences: A253568 A253569 A253570 * A253572 A253573 A253574

Keyword

nonn

Author

Marko Riedel, Jan 03 2015

Status

approved