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Search: id:A007863
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| A007863 |
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Number of hybrid binary trees with n nodes. |
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+0
5
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| 1, 2, 7, 31, 154, 820, 4575, 26398, 156233, 943174, 5785416, 35955297, 225914342, 1432705496, 9158708775, 58954911423, 381806076426, 2485972170888, 16263884777805, 106858957537838
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. S. S. Gu, N. Y. Li and T. Mansour, 2-Binary trees: bijections and related issues, Discr. Math., 308 (2008), 1209-1221.
J.M. Pallo, On the listing and random generation of hybrid binary trees, International Journal of Computer Mathematics, 50, 1994, 135-145.
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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G.f. satisfies x^2*A(x)^3+x*A(x)^2+(-1+x)*A(x)+1 = 0.
a(n) = 3F2({-n, n+1, n+2 } ; {1, 3/2})( -(1/4) ) [From Olivier GERARD (olivier.gerard(AT)gmail.com), Apr 23 2009]
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MAPLE
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A:= proc(n) option remember; if n=0 then 1 else convert (series ((x^2*A(n-1)^3 +x*A(n-1)^2 +1)/ (1-x), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n): seq (a(n), n=0..19); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 22 2008]
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MATHEMATICA
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InverseSeries[Series[(y-y^2-y^3)/(1+y), {y, 0, 24}], x] (* then A(x)=y(x)/x *) - Len Smiley Apr 14 2000
Table[ HypergeometricPFQ[{-n, 1 + n, 2 + n}, {1, 3/2}, -(1/4)], {n, 0, 20}] [From Olivier GERARD (olivier.gerard(AT)gmail.com), Apr 23 2009]
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PROGRAM
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(Macsyma) taylor_solve_choose_order:true; taylor_solve( A^3*X^2+A^2*X+A*(X-1)+1, A, X, 0, [ 20 ]);
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CROSSREFS
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Cf. A007788.
Sequence in context: A076177 A007164 A126033 this_sequence A030823 A030873 A030913
Adjacent sequences: A007860 A007861 A007862 this_sequence A007864 A007865 A007866
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KEYWORD
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nonn
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AUTHOR
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pallo(AT)u-bourgogne.fr (Jean Pallo)
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