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A036770
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Number of labeled rooted trees with a degree constraint: (2*n)!/(2^n)*C(2*n+1,n).
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4
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1, 3, 60, 3150, 317520, 52390800, 12843230400, 4382752374000, 1986847742880000, 1155153277710432000, 838011196011749760000, 742058914068404412480000, 787724078011075453248000000, 987468397792455300321600000000, 1443283810213452666950050560000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is the number of rooted labeled strictly binary trees ( each vertex has exactly two children or none) on 2n+1 vertices. - Geoffrey Critzer, Nov 13 2011
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REFERENCES
| L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10, esp. Eq. (12).
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 46
Index entries for sequences related to rooted trees
Eric Weisstein's World of Mathematics, Strongly Binary Tree.
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FORMULA
| E.g.f.: (1/2)/x*(2-2*(1-2*x^2)^(1/2)). Recurrence: {a(1)=1, a(2)=0, a(3)=3, (-2*n^3-6*n^2-4*n)*a(n)+(n+3)*a(n+2)}
E.g.f. satisfies G(x)= x(1+G(x)^2/2). - Geoffrey Critzer, Nov 13 2011
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MAPLE
| spec := [S, {S=Union(Z, Prod(Z, Set(S, card=2)))}, labeled]: seq(combstruct[count](spec, size=n)
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MATHEMATICA
| Range[0, 19]! CoefficientList[Series[(1 - (1 - 2 x^2)^(1/2))/x, {x, 0, 20}], x] (* Geoffrey Critzer, Nov 13 2011 *)
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CROSSREFS
| Cf. A036771, A052510, A001190.
Sequence in context: A081854 A085990 A202065 * A201699 A006821 A165626
Adjacent sequences: A036767 A036768 A036769 * A036771 A036772 A036773
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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