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A120348 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). 1

%I

%S 1,8,156,4896,212520,11793600,797448960,63606090240,5846743244160,

%T 608588457523200,70758332701056000,9088747467351552000,

%U 1278179579224720972800,195333707771834926694400

%N 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).

%D E. M. Palmer and R. C. Read, On the number of plane 2-trees, J. London Math. Soc. (2), 6, 1973, 583-592.

%F a(n) = (5n-2)!/(4n-1)!.

%F E.g.f. T = T(x) satisfies T(1-T)^4 = x.

%p seq((5*n-2)!/(4*n-1)!,n=1..16);

%K nonn

%O 1,2

%A _Emeric Deutsch_, Jun 24 2006

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Last modified September 19 11:06 EDT 2019. Contains 327192 sequences. (Running on oeis4.)