Search: id:A006964
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%I A006964 M2994
%S A006964 1,3,15,82,495,3144,20875,142773,1000131,7136812,51702231,
%T A006964 379234623,2810874950,21020047557,158398829121,1201617201230,
%U A006964 9169060501023,70329406653879,541949364313821,4193569906262874
%N A006964 Number of directed rooted trees with n nodes.
%D A006964 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006964 P. Leroux and B. Miloudi, ``G\'{e}n\'{e}ralisations de la formule d'Otter,
               '' Ann. Sci. Math. Qu\'{e}bec, Vol. 16, No. 1, pp. 53-80, 1992.
%H A006964 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=439">
               Encyclopedia of Combinatorial Structures 439</a>
%H A006964 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A006964 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A006964 a(n+1) has g.f.: prod from n =1 to inf ( 1 - x^3 a(n) )^-1.
%p A006964 with (numtheory): a:= proc(n) option remember; local d,j; if n<=1 then 
               n else (add (d*a(d)*3, d=divisors(n-1)) +add (add (d*a(d), d=divisors(j)) 
               *a(n-j)*3, j=1..n-2))/(n-1) fi end: seq (a(n), n=1..20); [From Alois 
               P. Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2008]
%Y A006964 Cf. A038059.
%Y A006964 Sequence in context: A084208 A059271 A014276 this_sequence A052451 A026019 
               A118356
%Y A006964 Adjacent sequences: A006961 A006962 A006963 this_sequence A006965 A006966 
               A006967
%K A006964 nonn,eigen
%O A006964 1,2
%A A006964 Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A006964 Also rooted trees with n nodes and 3-colored non-root nodes.
%E A006964 Extended with alternative description by Christian G. Bower (bowerc(AT)usa.net), 
               Apr 15 1998.

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