Search: id:A000151
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%I A000151 M1770 N0701
%S A000151 1,2,7,26,107,458,2058,9498,44947,216598,1059952,5251806,26297238,
%T A000151 132856766,676398395,3466799104,17873508798,92630098886,482292684506,
%U A000151 2521610175006,13233573019372,69687684810980,368114512431638,1950037285256658,
               10357028326495097,55140508518522726,294219119815868952,1573132563600386854,
               8427354035116949486,45226421721391554194
%N A000151 Number of oriented rooted trees with n nodes. Also rooted trees with 
               n nodes and 2-colored non-root nodes.
%D A000151 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like 
               Structures, Camb. 1998, p. 286.
%D A000151 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 60, R(x).
%D A000151 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               138.
%D A000151 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000151 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000151 N. J. A. Sloane, <a href="b000151.txt">Table of n, a(n) for n = 1..500</
               a>
%H A000151 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=387">
               Encyclopedia of Combinatorial Structures 387</a>
%H A000151 P. Leroux and B. Miloudi, <a href="http://www.labmath.uqam.ca/~annales/
               english/volumes/16-1/53.html">Generalisations de la formule d'Otter</
               a>, Ann. Sci. Math. Quebec 16 (1992), no 1, 53-80.
%H A000151 S. G. Wagner, <a href="http://finanz.math.tu-graz.ac.at/~wagner/identity.pdf">
               An identity for the cycle indices of rooted tree automorphism groups</
               a>, Elec. J. Combinat., 13 (2006), #R00.
%H A000151 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A000151 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000151 a(n+1) has g.f.: prod from n=1 to inf (1 - x^(2*a(n)))^(-1). [This doesn't 
               seem to make sense! - N. J. A. Sloane (njas(AT)research.att.com)]
%F A000151 Generating function A(x) = x+2*x^2+7*x^3+26*x^4+... satisfies A(x)=x*exp( 
               2*sum_{k>=1}(A(x^k)/k) ) [Harary]. - Pab Ter (pabrlos2(AT)yahoo.com), 
               Oct 12 2005
%p A000151 R:=series(x+2*x^2+7*x^3+26*x^4,x,5); M:=500;
%p A000151 for n from 5 to M do
%p A000151 series(add( subs(x=x^k,R)/k, k=1..n-1),x,n);
%p A000151 t4:=coeff(series(x*exp(%)^2,x,n+1),x,n);
%p A000151 R:=series(R+t4*x^n,x,n+1); od:
%p A000151 for n from 1 to M do lprint(n,coeff(R,x,n)); od: - N. J. A. Sloane (njas(AT)research.att.com), 
               Mar 10 2007
%p A000151 with(combstruct):norootree:=[S, {B = Set(S), S = Prod(Z,B,B)}, unlabeled] 
               :seq(count(norootree,size=i),i=1..30); # with Algolib (Pab Ter)
%Y A000151 Cf. A000238, A038055.
%Y A000151 Also the self-convolution of A005750. - Paul D. Hanna (pauldhanna(AT)juno.com), 
               Aug 17 2002
%Y A000151 Sequence in context: A150565 A150566 A150567 this_sequence A150568 A102319 
               A006603
%Y A000151 Adjacent sequences: A000148 A000149 A000150 this_sequence A000152 A000153 
               A000154
%K A000151 nonn,easy,eigen,nice
%O A000151 1,2
%A A000151 N. J. A. Sloane (njas(AT)research.att.com).
%E A000151 Extended with alternate description by Christian G. Bower (bowerc(AT)usa.net), 
               Apr 15 1998.
%E A000151 More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 12 2005

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