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%I #15 Dec 19 2015 09:54:51
%S 3,6,45,504,7785,153468,3681909,104126256,3392064945,125089571700,
%T 5151335388309,234322765501608,11668410187187481,631335472193760012,
%U 36881146426978035765,2313552152470193124192,155107536736245864549345
%N Number of labeled rooted trees with 3-colored leaves.
%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.83)
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Divides by n and shifts left under exponential transform.
%F E.g.f.: 2*x - LambertW(-x*exp(2*x)). - _Vladeta Jovovic_, Mar 09 2003
%F a(n) = Sum_{k=0..n} (binomial(n, k)*2^k*(n-k)^(n-1)).
%F a(n) ~ sqrt(1+LambertW(2*exp(-1))) * (2*exp(-1)/LambertW(2*exp(-1)))^n * n^(n-1). - _Vaclav Kotesovec_, Oct 05 2013
%t Rest[CoefficientList[Series[2*x-LambertW[-x*E^(2*x)], {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Oct 05 2013 *)
%Y Cf. A000169, A029857.
%Y Cf. A038049.
%K nonn,eigen
%O 1,1
%A _Christian G. Bower_, Jan 04 1999
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