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Search: id:A005264
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| A005264 |
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Number of labeled rooted Greg trees with n nodes.
(Formerly M3096)
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+0
9
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| 1, 3, 22, 262, 4336, 91984, 2381408, 72800928, 2566606784, 102515201984, 4575271116032, 225649908491264, 12187240730230528, 715392567595403520, 45349581052869924352, 3087516727770990992896, 224691760916830871873536
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A rooted Greg tree can be described as a rooted tree with 2-colored nodes where only the black nodes are counted and labeled and the white nodes have at least 2 children. (Christian G. Bower, Nov 15 1999)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Felsenstein, The number of evolutionary trees, Systematic Zoology, 27 (1978), 27-33.
L. R. Foulds and R. W. Robinson, Determining the asymptotic number of phylogenetic trees, pp. 110-126 of Combinatorial Mathematics VII (Newcastle, August 1979), ed. R. W. Robinson, G. W. Southern and W. D. Wallis. Lect. Notes in Math., 829. Springer, 1980.
C. Flight, How many stemmata?, Manuscripta, 34 (1990), 122-128.
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LINKS
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Index entries for reversions of series
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
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E.g.f. satisfies (1+x)e^A(x)=1+2A(x).
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PROGRAM
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(PARI) {a(n)= local(A); if(n<1, 0, for(k= 1, n, A+= x*O(x^k); A= truncate( (1+x)* exp(A) -1-A) ); n!* polcoeff( A, n))} /* Michael Somos Apr 02 2007 */
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CROSSREFS
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Inverse Stirling transform of A005172 (hence corrected and extended) - John Layman (layman(AT)calvin.math.vt.edu).
Exponential reversion of A005408 (odd numbers). Cf. A005263, A048159, A048160, A052300-A052303.
Sequence in context: A143634 A054595 A054594 this_sequence A052892 A155806 A074706
Adjacent sequences: A005261 A005262 A005263 this_sequence A005265 A005266 A005267
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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