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A036768
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Number of rooted trees with a degree constraint.
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0
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1, 1, 2, 5, 14, 42, 132, 428, 1421, 4807, 16510, 57421, 201824, 715768, 2558167, 9204651, 33315919, 121218195, 443107245, 1626546453, 5993256280, 22158739970, 82182744284, 305670888560, 1139892935454, 4261095044346, 15964169665031
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10, esp. Eq. (6).
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LINKS
| Index entries for sequences related to rooted trees
Vladimir Kruchinin, Compositae and their properties , arXiv:1103.2582
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FORMULA
| G.f. A(x) satisfies A(x)=1+sum(n=1..6, (x*A(x))^n) [From Vladimir Kruchinin, Feb 22 2011].
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MAPLE
| r := 6; [ seq((1/n)*add( (-1)^j*binomial(n, j)*binomial(2*n-2-j*(r+1), n-1), j=0..floor((n-1)/(r+1))), n=1..30) ]; end;
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PROG
| (PARI) a(n)=if(n<0, 0, polcoeff(serreverse(x/polcyclo(7)+O(x^(n+2))), n+1)) (from R. Stephan)
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CROSSREFS
| Sequence in context: A024175 A152226 A054393 * A058094 A080938 A054394
Adjacent sequences: A036765 A036766 A036767 * A036769 A036770 A036771
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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