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%I #17 Dec 19 2015 14:15:17
%S 1,1,1,0,4,5,96,1057,14848,235881,4234240,84815621,1877090304,
%T 45524670061,1201345331200,34283233751145,1052350187831296,
%U 34582597023733073,1211614017182760960,45088964565749965837
%N Number of labeled trimmed trees with n nodes.
%C A trimmed tree is a tree with a forbidden limb of length 2.
%C A tree with a forbidden limb of length k is a tree where the path from any leaf inward hits a branching node or another leaf within k steps.
%H Vincenzo Librandi, <a href="/A052320/b052320.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F E.g.f.: 1 + x^3/2 + x^4/2 + B(x) - B(x)^2/2 where B(x) is e.g.f. of A052318.
%F a(n) ~ (1+LambertW(-2*exp(-2)))^(3/2) * exp((n*LambertW(-2*exp(-2)))/2) * n^(n-2). - _Vaclav Kotesovec_, Mar 29 2014
%t CoefficientList[Series[1+x^3/2+x^4/2-LambertW[-x/E^(x^2)]-(LambertW[-x/E^(x^2)])^2/2, {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Mar 29 2014 *)
%Y Cf. A002955, A002988-A002992, A052318-A052329.
%K nonn
%O 0,5
%A _Christian G. Bower_, Dec 15 1999
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