Search: id:A000220
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%I A000220 M2583 N1022
%S A000220 1,0,0,0,0,0,1,1,3,6,15,29,67,139,310,667,1480,3244,7241,16104,
%T A000220 36192,81435,184452,418870,955860,2187664,5025990,11580130,26765230,
%U A000220 62027433,144133676,335731381,783859852,1834104934,4300433063,10102854473
%N A000220 Number of asymmetric trees with n nodes (also called identity trees).
%D A000220 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000220 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000220 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like 
               Structures, Camb. 1998, p. 330.
%D A000220 F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969, p. 232.
%D A000220 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 66, Eq. (3.3.22).
%D A000220 F. Harary, R. W. Robinson and A. J. Schwenk, Twenty-step algorithm for 
               determining the asymptotic number of trees of various species, J. 
               Austral. Math. Soc., Series A, 20 (1975), 483-503. Errata: Vol. A 
               41 (1986), p. 325.
%D A000220 D. E. Knuth, Fundamental Algorithms, 3d Ed. 1997, pp. 386-88 describes 
               methodology for generating similar sequence rapidly.
%D A000220 R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
%D A000220 A. J. Schwenk, personal communication.
%H A000220 T. D. Noe, <a href="b000220.txt">Table of n, a(n) for n=1..200</a>
%H A000220 E. Friedman, <a href="a000220.gif">Illustration of initial terms</a>
%H A000220 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000220 G.f.: A(x)-A^2(x)/2-A(x^2)/2, where A(x) is g.f. for A004111
%t A000220 s[ n_, k_ ] := s[ n, k ]=a[ n+1-k ]+If[ n<2k, 0, -s[ n-k, k ] ]; a[ 1 
               ]=1; a[ n_ ] := a[ n ]=Sum[ a[ i ]s[ n-1, i ]i, {i, 1, n-1} ]/(n-1); 
               Table[ a[ i ]-Sum[ a[ j ]a[ i-j ], {j, 1, i/2} ]+If[ OddQ[ i ], 0, 
               a[ i/2 ](a[ i/2 ]-1)/2 ], {i, 1, 50} ] (from Robert A. Russell)
%Y A000220 Cf. A000055, A000081.
%Y A000220 Sequence in context: A066708 A034464 A116696 this_sequence A092641 A077449 
               A152232
%Y A000220 Adjacent sequences: A000217 A000218 A000219 this_sequence A000221 A000222 
               A000223
%K A000220 nonn,easy,nice
%O A000220 1,9
%A A000220 N. J. A. Sloane (njas(AT)research.att.com).

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