%I A005640 M1896
%S A005640 1,1,2,8,64,832,15104,352256,10037248,337936384,13126565888,
%T A005640 577818263552,28425821618176,1545553369366528,92034646352592896,
%U A005640 5956917762776367104,416397789920380321792,31262503202358260924416
%N A005640 Number of phylogenetic trees with n labels.
%C A005640 Each node of the tree is a subset of the labeled set {1,...,n}. If the 
               subset node is empty, it must have degree at least 3.
%D A005640 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005640 L. R. Foulds and R. W. Robinson, Determining the asymptotic number of 
               phylogenetic trees, pp. 110-126 of Combinatorial Mathematics VII 
               (Newcastle, August 1979), ed. R. W. Robinson, G. W. Southern and 
               W. D. Wallis. Lect. Notes Math., 829. Springer, 1980.
%D A005640 J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 
               (1976), 700-709.
%D A005640 K. L. Kodandapani and S. C. Seth, On combinational networks with restricted 
               fan-out, IEEE Trans. Computers, 27 (1978), 309-318.
%D A005640 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 5.26.
%H A005640 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A005640 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A005640 STIRLING transform of A005263. E.g.f.: 1+B(x)-B(x)^2 where B(x) is e.g.f. 
               of A005172.
%Y A005640 For n >= 2, A005640(n) = 2^n*A006351(n) = 2^(n+1)*A000311(n).
%Y A005640 Sequence in context: A136282 A092934 A139679 this_sequence A153540 A153568 
               A153531
%Y A005640 Adjacent sequences: A005637 A005638 A005639 this_sequence A005641 A005642 
               A005643
%K A005640 nonn,nice,easy
%O A005640 0,3
%A A005640 N. J. A. Sloane (njas(AT)research.att.com).
%E A005640 More terms, formula and comment from Christian G. Bower (bowerc(AT)usa.net), 
               Nov 15 1999.