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A005354
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Number of asymmetric planar trees with n nodes.
(Formerly M2808)
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3
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1, 1, 0, 0, 0, 1, 3, 9, 28, 85, 262, 827, 2651, 8626, 28507, 95393, 322938, 1104525, 3812367, 13266366, 46504495, 164098390, 582521687, 2079133141, 7457788295, 26872946466, 97238824018, 353218128299, 1287657977946, 4709784136316
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| a(13) in the Labelle table is a typographic error. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 03 2010]
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REFERENCES
| G. Labelle, Counting asymmetric enriched trees. J. Symbolic Comput. 14 (1992), no. 2-3, 211-242.
Torsten Muetze and Franziska Weber, Construction of 2-factors in the middle layer of the discrete cube, Arxiv preprint arXiv:1111.2413, 2011
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for sequences related to trees
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FORMULA
| G.f.: 1+B(x)+(C(x^2)-C(x)^2)/2 where B is g.f. of A022553(n-1) and C is g.f. of A000108(n-1).
a(n)=A022553(n-1) - A000108(n-2)/2 - (if n is even) A000108(n/2-1)/2.
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MAPLE
| Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 03 2010: (Start)
A000108 := proc(n) binomial(2*n, n)/(n+1) ; end proc:
A007727 := proc(n) local a, d; a := 0 ; for d in numtheory[divisors](n) do a := a+binomial(2*d, d)*numtheory[mobius](n/d) ; end do ; a ; end proc;
A022553 := proc(n) A007727(n)/2/n ; end proc:
A005354 := proc(n) local a; if n <=1 then 1; else a := A022553(n-1) ; a := a-A000108(n-1)/2 ; if type(n, 'even') then a := a-A000108(n/2-1)/2 ; end if; a ; end if; end proc: seq(A005354(n), n=0..20) ; (End)
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CROSSREFS
| Cf. A000108, A002995, A022553.
Sequence in context: A027099 A027090 A033139 * A084084 A091140 A052541
Adjacent sequences: A005351 A005352 A005353 * A005355 A005356 A005357
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe, Susanna Cuyler
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EXTENSIONS
| More terms, formula from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
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