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A052510
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Number of labeled planar binary trees with n elements (external nodes or internal nodes).
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2
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OFFSET
| 1,2
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 54
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FORMULA
| E.g.f.: (1/2)/x*(1-(1-4*x^2)^(1/2))
Recurrence: {a(1)=1, a(2)=0, (-4*n^3-12*n^2-8*n)*a(n)+(n+3)*a(n+2), a(3)=6}
a(n) = (2n-1)/n * ( (2(n-1))! / (n-1)! )^2 - Travis Kowalski (kowalski(AT)euclid.UCSD.Edu), Dec 15, 2000
I*sin(asec(2x)) = -1/2x + x + 6x^3/3! + 240x^5/5! + 25200x^7/7! +...
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MAPLE
| spec := [S, {S=Union(Z, Prod(Z, S, S))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
| Equals 2^(n-1) * A036770(n). Cf. A101921.
Sequence in context: A172965 A002022 A065948 * A137892 A064382 A080358
Adjacent sequences: A052507 A052508 A052509 * A052511 A052512 A052513
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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