%I A005804 M1890
%S A005804 1,2,8,58,612,8374,140408,2785906,63830764,1658336270,48169385024,
%T A005804 1546832023114,54413083601268,2080827594898342,85948745163598088,
%U A005804 3813417859420469410,180876816831806597500,9133309115320844870078
%N A005804 Number of phylogenetic rooted trees with n labels.
%C A005804 These are series-reduced rooted trees where each leaf is a non-empty 
               subset of the set of n labels.
%C A005804 See A141268 for phylogenetic rooted trees with n unlabeled objects. - 
               Thomas Wieder (thomas.wieder(AT)t-online.de), Jun 20 2008
%D A005804 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005804 Foulds, L. R.; Robinson, R. W. Enumeration of phylogenetic trees without 
               points of degree two. Ars Combin. 17 (1984), A, 169-183. Math. Rev. 
               85f:05045
%H A005804 T. D. Noe, <a href="b005804.txt">Table of n, a(n) for n=1..100</a>
%H A005804 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A005804 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A005804 Stirling transform of [ 1, 1, 4, 26, 236, ... ] = A000311 [ Foulds and 
               Robinson ].
%F A005804 G.f.: -LambertW(-1/2*exp(1/2*exp(z)-1))+1/2*exp(z)-1 series(-LambertW(-1/
               2*exp(1/2*exp(z)-1))+1/2*exp(z)-1,z=0,10). - Thomas Wieder (thomas.wieder(AT)t-online.de), 
               Jun 20 2008
%e A005804 a(3)=8 because we have:
%e A005804 Set(Set(Z[3]),Set(Z[1]),Set(Z[2])),
%e A005804 Set(Z[3],Z[2],Z[1]),
%e A005804 Set(Set(Z[3],Z[1]),Set(Z[2])),
%e A005804 Set(Set(Set(Z[3]),Set(Z[2])),Set(Z[1])),
%e A005804 Set(Set(Set(Z[3]),Set(Z[1])),Set(Z[2])),
%e A005804 Set(Set(Z[3]),Set(Set(Z[1]),Set(Z[2]))),
%e A005804 Set(Set(Z[3]),Set(Z[2],Z[1])),
%e A005804 Set(Set(Z[3],Z[2]),Set(Z[1]))
%p A005804 combstruct command: A005804 := [H, {H=Union(Set(Z,card>=1),Set(H,card>
               =2))}, labelled]; seq(count(A00584,size=j),j=1..20); - Thomas Wieder 
               (thomas.wieder(AT)t-online.de), Jun 20 2008
%Y A005804 Cf. A000311, A005805.
%Y A005804 Cf. A141268.
%Y A005804 Sequence in context: A153553 A007347 A063074 this_sequence A162067 A086907 
               A132186
%Y A005804 Adjacent sequences: A005801 A005802 A005803 this_sequence A005805 A005806 
               A005807
%K A005804 nonn,easy
%O A005804 1,2
%A A005804 N. J. A. Sloane (njas(AT)research.att.com).
%E A005804 More terms, comment from Christian G. Bower (bowerc(AT)usa.net), Dec 
               15 1999.