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A206855 The sum of the degree of each root node over all rooted labelled trees on n nodes. 0
0, 0, 2, 12, 96, 1000, 12960, 201684, 3670016, 76527504, 18000000000, 47158953820, 1362182012928, 43011849456888, 1474041721757696, 54493461914062500, 2161727821137838080, 91597537648314105376, 4128944057284204560384, 197293926880252878693804, 9961472000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The mean root degree approaches 2 as n -> infinity.

LINKS

Table of n, a(n) for n=0..20.

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 179.

FORMULA

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)).

a(n) = 2*A053506(n). - R. J. Mathar, Nov 07 2014

MATHEMATICA

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

CROSSREFS

Sequence in context: A014297 A052564 A193425 * A219119 A052611 A059864

Adjacent sequences:  A206852 A206853 A206854 * A206856 A206857 A206858

KEYWORD

nonn,easy

AUTHOR

Geoffrey Critzer, Feb 13 2012

STATUS

approved

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Last modified December 3 16:24 EST 2016. Contains 278745 sequences.