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A005753
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Number of rooted identity matched trees with n nodes.
(Formerly M1514)
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3
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1, 2, 5, 18, 66, 266, 1111, 4792, 21124, 94888, 432415, 1994828, 9296712, 43706722, 207030398, 987130456, 4733961435, 22819241034, 110500644857, 537295738556, 2622248720234, 12840953621208, 63074566121245
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1991), 93-104.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 429
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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FORMULA
| G.f.: x*Product_{n>=1} (1 + x^n)^(2*a(n)) = Sum_{n>=1} a(n)*x^n. [From Paul D. Hanna, Dec 31 2011]
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EXAMPLE
| G.f.: A(x) = x + 2*x^2 + 5*x^3 + 18*x^4 + 66*x^5 + 266*x^6 +...
where A(x) = x*(1+x)^2*(1+x^2)^4*(1+x^3)^10*(1+x^4)^36*(1+x^5)^132*...
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PROG
| (PARI) {a(n)=polcoeff(x*prod(k=1, n-1, (1+x^k+x*O(x^n))^(2*a(k))), n)} /* Paul D. Hanna */
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CROSSREFS
| Cf. A038077.
Sequence in context: A150017 A150018 A150019 * A150020 A144721 A150021
Adjacent sequences: A005750 A005751 A005752 * A005754 A005755 A005756
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KEYWORD
| nonn,eigen
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Also rooted identity trees with n nodes and 2-colored non-root nodes.
Extended with alternative description by Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
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