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A206855
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The sum of the degree of each root node over all rooted labelled trees on n nodes.
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0
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0, 0, 2, 12, 96, 1000, 12960, 201684, 3670016, 76527504, 18000000000, 47158953820, 1362182012928, 43011849456888, 1474041721757696, 54493461914062500, 2161727821137838080, 91597537648314105376, 4128944057284204560384, 197293926880252878693804, 9961472000000000000000000
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OFFSET
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0,3
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COMMENTS
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The mean root degree approaches 2 as n -> infinity.
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REFERENCES
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P Flajolet and R Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 179.
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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a(n) = Sum_{k=0..n} A206429(n,k)*k.
E.g.f.: T(x)^2 where T(x) is the e.g.f. for A000169.
a(n) = 2*(n^(n-1)-n^(n-2))
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MATHEMATICA
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nn=15; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; D[ Range[0, nn]!CoefficientList[Series[x Exp[y t], {x, 0, nn}], x], y]/.y->1
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CROSSREFS
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Sequence in context: A014297 A052564 A193425 * A219119 A052611 A059864
Adjacent sequences: A206852 A206853 A206854 * A206856 A206857 A206858
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KEYWORD
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nonn
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AUTHOR
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Geoffrey Critzer, Feb 13 2012
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STATUS
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approved
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