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Search: id:A061575
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| A061575 |
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Number of planar planted trees with n non-root nodes and without isolated 2-valent nodes. |
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+0
1
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| 0, 1, 0, 2, 2, 7, 14, 41, 107, 307, 871, 2546, 7497, 22380, 67366, 204517, 625132, 1922700, 5945469, 18473841, 57649699, 180602285, 567772883, 1790663427, 5663969707, 17963483548, 57112388657, 181994536484, 581168157605
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OFFSET
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0,4
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COMMENT
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An isolated 2-valent node is a 2-valent node non-adjacent to any other 2-valent node.
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.7.11).
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FORMULA
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G.f.: Sum_{i >= 0} 1/(i+1)*binomial(2*i, i)*x^(i+1)*((1+x^3)/(1-x^2))^(i+1)*(1+x*(1+x^3)/(1-x^2))^(-(i+1)) or (1-x^2+x^3-sqrt((1-x^2+x^3)*(1-4*x+3*x^2-3*x^3)))/(2-2*x^2+2*x^3).
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CROSSREFS
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Sequence in context: A156435 A162460 A061274 this_sequence A133602 A137249 A051769
Adjacent sequences: A061572 A061573 A061574 this_sequence A061576 A061577 A061578
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 13 2001
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