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A036774
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Number of labeled rooted binary trees (each node has out-degree <=2).
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6
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0, 1, 2, 9, 60, 540, 6120, 83790, 1345680, 24811920, 516650400, 11992503600, 307069963200, 8598348158400, 261387760233600, 8573572885878000, 301809119163552000, 11349727401396384000, 454104511068656448000, 19261139319649202976000
(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. (14) with r = 2.
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LINKS
| Index entries for sequences related to rooted trees
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FORMULA
| E.g.f. (1-x-sqrt(1-2x-x^2))/x.
E.g.f. A(x) satisfies x*A(x)^2 +2(x-1)A(x)+2x=0, A(0)=0 and A(x)=x/(1-x-(x/2)A(x)). - Michael Somos, Sep 06 2003
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MATHEMATICA
| Range[0, 20]! CoefficientList[Series[(1 - x - ((x - 1)^2 - 2 x^2)^(1/2))/x, {x, 0, 20}], x] (*Geoffrey Critzer, Nov 22 2011*)
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PROG
| (PARI) a(n)=if(n<1, 0, n!*polcoeff(2*x/(1-x+sqrt(1-2*x-x^2+O(x^n))), n))
(PARI) a(n)=if(n<1, 0, n!*polcoeff(serreverse(2*x/(2+2*x+x^2)+x*O(x^n)), n))
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CROSSREFS
| A071356(n)=a(n+1)2^n/(n+1)!.
Sequence in context: A001193 A161391 A120014 * A166882 A053983 A192939
Adjacent sequences: A036771 A036772 A036773 * A036775 A036776 A036777
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description and formula from Christian G. Bower (bowerc(AT)usa.net), Nov 29 2001
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