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A206855
The sum of the degree of each root node over all rooted labeled trees on n nodes.
0
0, 0, 2, 12, 96, 1000, 12960, 201684, 3670016, 76527504, 1800000000, 47158953820, 1362182012928, 43011849456888, 1474041721757696, 54493461914062500, 2161727821137838080, 91597537648314105376, 4128944057284204560384, 197293926880252878693804, 9961472000000000000000000
OFFSET
0,3
COMMENTS
The mean root degree approaches 2 as n -> infinity.
LINKS
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: A052564 A014297 A193425 * A219119 A052611 A340938
KEYWORD
nonn,easy
AUTHOR
Geoffrey Critzer, Feb 13 2012
EXTENSIONS
a(10) corrected by Georg Fischer, Mar 23 2023
STATUS
approved