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A036771
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Number of labeled rooted trees with a degree constraint: (3*n)!/(6^n))*binomial(3*n+1,n).
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1
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1, 4, 420, 201600, 264264000, 734557824000, 3723191087616000, 31125877492469760000, 399532678960326912000000, 7462849882264211635200000000, 194563959280510261541299200000000, 6847568575944052279580806348800000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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
| Index entries for sequences related to rooted trees
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 47
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FORMULA
| E.g.f.: -(1/2)/x*((-3*x+((-8+9*x^3)/x)^(1/2))*x^2)^(1/3)-1/((-3*x+((-8+9*x^3)/x)^(1/2))*x^2)^(1/3)-1/2*I*3^(1/2)*(1/x*((-3*x+((-8+9*x^3)/x)^(1/2))*x^2)^(1/3)-2/((-3*x+((-8+9*x^3)/x)^(1/2))*x^2)^(1/3))
Recurrence: {a(0)=0, a(2)=0, (-9*n^4-45*n^3-63*n^2-27*n)*a(n)+(8*n+28)*a(n+3)}
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MAPLE
| spec := [S, {S=Union(Z, Prod(Z, Set(S, card=3)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
| Cf. A036770.
Sequence in context: A202172 A158111 A198709 * A201980 A080321 A172858
Adjacent sequences: A036768 A036769 A036770 * A036772 A036773 A036774
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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