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A036776
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Number of labeled rooted trees with a degree constraint.
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0
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1, 2, 9, 64, 625, 7770, 117390, 2088520, 42771960, 991090800, 25635767850, 732235165200, 22890759391500, 777398836414200, 28501053507927000, 1121908690738836000, 47194400446765572000, 2112854517933207048000
(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. (14) with r = 4.
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LINKS
| Index entries for sequences related to rooted trees
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FORMULA
| E.g.f. A(x) satisfies A(x)=1+x*A(x)+1/2*x^2*A(x)^2+1/6*x^3*A(x)^3+1/24*A(x)^4. a(n)=(n!*sum(r=0..n+1, binomial(n+1,r)*sum(m=0..r, binomial(r,m) *sum(j=0..m, binomial(j,-r+n-m-j)*2^(2*r-2*n+m+2*j)*binomial(m,j)*(3)^(-j))))); [From Vladimir Kruchinin, Nov 22 2011]
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PROG
| (Maxima)
a(n):=(n!*sum(binomial(n+1, r)*sum(binomial(r, m)*sum(binomial(j, -r+n-m-j)*2^(2*r-2*n+m+2*j)*binomial(m, j)*(3)^(-j), j, 0, m), m, 0, r), r, 0, n+1)); [From Vladimir Kruchinin, Nov 22 2011]
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CROSSREFS
| Sequence in context: A141209 A128577 A052514 * A036777 A055860 A152917
Adjacent sequences: A036773 A036774 A036775 * A036777 A036778 A036779
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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