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A120348
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Number of labeled simply-rooted 2-trees with n labeled vertices (i.e., n+2 vertices altogether; a simply-rooted 2-tree is an externally rooted 2-tree whose root edge belongs to exactly one triangle).
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1
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1, 8, 156, 4896, 212520, 11793600, 797448960, 63606090240, 5846743244160, 608588457523200, 70758332701056000, 9088747467351552000, 1278179579224720972800, 195333707771834926694400
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OFFSET
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1,2
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REFERENCES
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E. M. Palmer and R. C. Read, On the number of plane 2-trees, J. London Math. Soc. (2), 6, 1973, 583-592.
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LINKS
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FORMULA
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a(n) = (5n-2)!/(4n-1)!.
E.g.f. T = T(x) satisfies T(1-T)^4 = x.
D-finite with recurrence -8*(4*n-3)*(2*n-1)*(4*n-1)*a(n) +5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-6)*a(n-1)=0. - R. J. Mathar, Jul 24 2022
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MAPLE
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seq((5*n-2)!/(4*n-1)!, n=1..16);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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