A206855 - OEIS

%I #33 Mar 23 2023 19:05:15

%S 0,0,2,12,96,1000,12960,201684,3670016,76527504,1800000000,

%T 47158953820,1362182012928,43011849456888,1474041721757696,

%U 54493461914062500,2161727821137838080,91597537648314105376,4128944057284204560384,197293926880252878693804,9961472000000000000000000

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

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

%H Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009, page 179.

%F a(n) = Sum_{k=0..n} A206429(n,k)*k.

%F E.g.f.: T(x)^2 where T(x) is the e.g.f. for A000169.

%F a(n) = 2*(n^(n-1) - n^(n-2)).

%F a(n) = 2*A053506(n). - _R. J. Mathar_, Nov 07 2014

%t 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

%K nonn,easy

%O 0,3

%A _Geoffrey Critzer_, Feb 13 2012

%E a(10) corrected by _Georg Fischer_, Mar 23 2023