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, 8, 156, 4896, 212520, 11793600, 797448960, 63606090240, 5846743244160, 608588457523200, 70758332701056000, 9088747467351552000, 1278179579224720972800, 195333707771834926694400

Offset

1,2

References

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

Links

Table of n, a(n) for n=1..14.

Formula

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

Maple

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

Crossrefs

Sequence in context: A268543 A345317 A113668 * A251586 A221098 A171211

Adjacent sequences: A120345 A120346 A120347 * A120349 A120350 A120351

Keyword

nonn

Author

Emeric Deutsch, Jun 24 2006

Status

approved