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Search: id:A000151
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| A000151 |
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Number of oriented rooted trees with n nodes. Also rooted trees with n nodes and 2-colored non-root nodes.
(Formerly M1770 N0701)
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+0
7
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| 1, 2, 7, 26, 107, 458, 2058, 9498, 44947, 216598, 1059952, 5251806, 26297238, 132856766, 676398395, 3466799104, 17873508798, 92630098886, 482292684506, 2521610175006, 13233573019372, 69687684810980, 368114512431638, 1950037285256658, 10357028326495097, 55140508518522726, 294219119815868952, 1573132563600386854, 8427354035116949486, 45226421721391554194
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 286.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 60, R(x).
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..500
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 387
P. Leroux and B. Miloudi, Generalisations de la formule d'Otter, Ann. Sci. Math. Quebec 16 (1992), no 1, 53-80.
S. G. Wagner, An identity for the cycle indices of rooted tree automorphism groups, Elec. J. Combinat., 13 (2006), #R00.
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
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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)]
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
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MAPLE
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R:=series(x+2*x^2+7*x^3+26*x^4, x, 5); M:=500;
for n from 5 to M do
series(add( subs(x=x^k, R)/k, k=1..n-1), x, n);
t4:=coeff(series(x*exp(%)^2, x, n+1), x, n);
R:=series(R+t4*x^n, x, n+1); od:
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
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)
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CROSSREFS
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Cf. A000238, A038055.
Also the self-convolution of A005750. - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 17 2002
Adjacent sequences: A000148 A000149 A000150 this_sequence A000152 A000153 A000154
Sequence in context: A150565 A150566 A150567 this_sequence A150568 A102319 A006603
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KEYWORD
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nonn,easy,eigen,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Extended with alternate description by Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 12 2005
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