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A253571
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Total number of even outdegree nodes among all labeled rooted trees on n nodes.
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1
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1, 2, 15, 144, 1765, 26400, 466459, 9508352, 219651849, 5671088640, 161833149511, 5058050224128, 171837337744813, 6304955850432512, 248477268083174355, 10467916801317273600, 469451601966727952401, 22329535184262444220416, 1122809130124800181976575
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OFFSET
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1,2
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LINKS
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FORMULA
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E.g.f.: (T^2+z^2)/(2*T*(1-T)) where T is the labeled tree function defined by T = z exp T.
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EXAMPLE
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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.
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MAPLE
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a:= n-> n!*coeff(series((T->(T^2+x^2)/
(2*T*(1-T)))(-LambertW(-x)), x, n+2), x, n):
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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