A206855 The sum of the degree of each root node over all rooted labeled trees on n nodes.

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

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: A052564 A014297 A193425 * A219119 A052611 A340938

Adjacent sequences: A206852 A206853 A206854 * A206856 A206857 A206858

Keyword

nonn,easy

Author

Geoffrey Critzer, Feb 13 2012

Extensions

a(10) corrected by Georg Fischer, Mar 23 2023

Status

approved