Search: id:A005805
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%I A005805 M1519
%S A005805 1,2,5,18,107,1008,13113,214238,4182487,94747196,2440784645,
%T A005805 70431957258,2249856084803,78802876705608,3002702793753489,
%U A005805 123649410977736950,5471808106109912815,258948617502187143188
%N A005805 Number of phylogenetic trees with n labels.
%C A005805 Series-reduced trees where each leaf is a non-empty subset of the set 
               of n labels.
%D A005805 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
%D A005805 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005805 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A005805 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A005805 Stirling transform of [ 1, 1, 1, 4, 26, 236, ... ] = A000311(n-1).
%p A005805 stirtr:= proc(p) proc (n) add (p(k) *combinat[stirling2] (n,k), k=0..n) 
               end end: b:= proc(n) option remember; if n<=1 then n elif n=2 then 
               1 else (n+1) *b(n-1) +2*add (binomial(n-1, k) *b(k) *b(n-k), k=2..n-2) 
               fi end: a:= stirtr (n->`if` (n<2,1, b(n-1))): seq (a(n), n=1..20); 
               [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 15 2008]
%Y A005805 Cf. A000311, A005804.
%Y A005805 Sequence in context: A005639 A093730 A007769 this_sequence A058338 A006896 
               A125625
%Y A005805 Adjacent sequences: A005802 A005803 A005804 this_sequence A005806 A005807 
               A005808
%K A005805 nonn,easy
%O A005805 1,2
%A A005805 N. J. A. Sloane (njas(AT)research.att.com).
%E A005805 More terms, comment from Christian G. Bower (bowerc(AT)usa.net), Dec 
               15 1999.

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