Search: id:A007827
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%I A007827
%S A007827 1,1,1,1,2,3,7,13,32,73,190,488,1350,3741,10765,31311,92949,278840,
%T A007827 847511,2599071,8044399,25082609,78758786,248803504,790411028,
%U A007827 2523668997,8095146289,26076714609,84329102797,273694746208
%N A007827 Number of homeomorphically irreducible (or series-reduced) trees with 
               n pendant nodes, or continua with n non-cut points, or leaves.
%C A007827 Also, number of unrooted multifurcating tree shapes with n leaves [see 
               Felsenstein].
%D A007827 M. Cropper, J. Combin. Math. Combin. Comp., Vol. 24 (1997), 177-184.
%D A007827 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 62.
%D A007827 S. B. Nadler Jr., Continuum Theory, Academic Press.
%D A007827 Joseph Felsenstein, Inferring Phylogenies. Sinauer Associates, Inc., 
               2004, pg. 33 (Beware errors!).
%H A007827 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A007827 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%H A007827 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A007827 G.f.: 1+(1+x-B(x))*B(x) where B(x) = x+x^2+2*x^3+5*x^4+12*x^5+33*x^6+90*x^7+... 
               is g.f. for A000669.
%p A007827 A := series(1+(1+x-B)*B,x,30); # where B = g.f. for A000669; A007827 
               := n->coeff(A,x,n);
%Y A007827 Cf. A000014 (series-reduced trees), A000055 (trees), A000311, A000669 
               (series-reduced planted trees by leaves), A059123 (homeomorphically 
               irreducible rooted trees by nodes)
%Y A007827 Number of row entries of A064060.
%Y A007827 Sequence in context: A002013 A003120 A032131 this_sequence A129859 A056953 
               A045611
%Y A007827 Adjacent sequences: A007824 A007825 A007826 this_sequence A007828 A007829 
               A007830
%K A007827 nonn,nice,easy
%O A007827 0,5
%A A007827 Matthew Cropper (mmcrop01(AT)athena.louisville.edu).
%E A007827 Corrected and extended by Christian G. Bower (bowerc(AT)usa.net), Nov 
               15 1999.

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