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%I #17 Nov 05 2021 09:47:57
%S 1,1,1,6,56,730,12372,259574,6511920,190413234,6364960940,
%T 239556803662,10028763883272,462366507311306,23282257730716740,
%U 1271520006077859750,74865320814990626912,4727699146425478764898,318763676354643090937692,22856568223852002933212798
%N Number of labeled trees with n nodes and 2-colored internal (non-leaf) nodes.
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F E.g.f.: 1 + B(x) - x*B(x) - B(x)^2/2 where B(x) is e.g.f. of A052316.
%F a(n) ~ (1+LambertW(-exp(-1)/2))^(3/2) * n^(n-2) / (exp(n)*(-LambertW(-exp(-1)/2))^n). - _Vaclav Kotesovec_, Oct 05 2013
%t CoefficientList[Series[1+(1-x)*(-x-LambertW[-2*x*E^(-x)])-(-x-LambertW[-2*x*E^(-x)])^2/2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 05 2013 *)
%Y Cf. A004113, A004114, A052316.
%K nonn
%O 0,4
%A _Christian G. Bower_, Dec 15 1999
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