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 A253571 Total number of even outdegree nodes among all labeled rooted trees on n nodes. 1
 1, 2, 15, 144, 1765, 26400, 466459, 9508352, 219651849, 5671088640, 161833149511, 5058050224128, 171837337744813, 6304955850432512, 248477268083174355, 10467916801317273600, 469451601966727952401, 22329535184262444220416, 1122809130124800181976575 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Marko Riedel and 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 6x1 and trees consisting of a node with two children, of which there are 3, and they have 3 even degree nodes, giving 3x3 for a total of 6x1+3x3 = 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: A005415 A219868 A224885 * A111686 A001854 A060226 Adjacent sequences:  A253568 A253569 A253570 * A253572 A253573 A253574 KEYWORD nonn AUTHOR Marko Riedel, Jan 03 2015 STATUS approved

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Last modified October 23 22:28 EDT 2019. Contains 328373 sequences. (Running on oeis4.)