%I A003214 M0775
%S A003214 1,1,2,3,6,10,20,37,76,152,320,672,1454,3154,6959,15439,34608,77988,176985,
%T A003214 403510,924683,2127335,4913452,11385955,26468231,61700232,144206269,337837221,
%U A003214 793213550,1866181155,4398867672,10387045476,24567374217,58196129468,138056734916
%N A003214 Number of binary forests with n nodes.
%C A003214 From Piet Hut, Nov 07, 2003: "Number of ways to place n stars in stable 
               hierarchical multiple star systems (where each stable multiple is 
               a binary tree: around its center of mass two multiple star systems 
               revolve, each of which can be a singleton or a nontrivial multiple 
               star system).
%C A003214 "For example, a(1) = 1 : *; a(2) = 2 : (**), * *; a(3) = 3 : ((**)*), 
               (**) *, * * *; a(4) = 6 : (((**)*)*), ((**)(**)), ((**)*) *, (**) 
               (**), (**) * *, * * * * ."
%D A003214 L. F. Meyers, Corrections and additions to Tree Representations in Linguistics. 
               Report 3, 1966, p. 138. Project on Linguistic Analysis, Ohio State 
               University Research Foundation, Columbus, Ohio.
%D A003214 L. F. Meyers and W. S.-Y. Wang, Tree Representations in Linguistics. 
               Report 3, 1963, pp. 107-108. Project on Linguistic Analysis, Ohio 
               State University Research Foundation, Columbus, Ohio.
%D A003214 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003214 T. D. Noe, <a href="b003214.txt">Table of n, a(n) for n=0..200</a>
%H A003214 Piet Hut, <a href="http://www.sns.ias.edu/~piet/">Home Page</a>
%F A003214 Euler transform of A001190. - Michael Somos, Nov 10 2003
%F A003214 G.f.: exp( sum G001190(x^i)/i, i=1..infinity ), where G001190 = g.f. 
               for A001190.
%Y A003214 Cf. A001190.
%Y A003214 Sequence in context: A045690 A007148 A093371 this_sequence A123423 A005195 
               A052843
%Y A003214 Adjacent sequences: A003211 A003212 A003213 this_sequence A003215 A003216 
               A003217
%K A003214 nonn,easy,nice
%O A003214 0,3
%A A003214 N. J. A. Sloane (njas(AT)research.att.com).