A339234 Number of series-reduced tanglegrams with n unlabeled leaves.

1, 1, 5, 51, 757, 16416, 461231, 16021550, 662197510, 31749450007, 1732478051823, 106025572201434, 7192665669790893, 535756912504764218, 43471544417828923777, 3816784803681841133512, 360546156617986177328681, 36462349359125513109697520, 3930704977357944446111295571

Offset: 1

Author

Andrew Howroyd, Jan 01 2021

Keywords

• nonn

Comments

A tanglegram is a pair of trees with their leaves superimposed. The original tanglegram sequence (A258620) used rooted binary trees. This variation uses planted series-reduced trees.

Examples

			Two of the 5 tanglegrams for a(3) are illustrated (A,B are the roots of the trees and o marks the leaves that are shared between the two trees)
           A             A
          /  \          /  \
         /   / \       /   / \
        o   o   o     o   o   o
         \  |  /       \ /   /
          \ | /          \  /
            B              B
		

Crossrefs

Cf. A000669 (series-reduced trees), A258620 (binary tanglegrams), A339645.

Programs

PARI

\\ See links in A339645 for combinatorial species functions.
seriesReducedTrees(n)={my(v=vector(n)); v[1]=sv(1); for(n=2, #v, v[n] = polcoef( sExp(x*Ser(v[1..n])), n )); x*Ser(v)}
NumUnlabeledObjsSeq(sCartPower(seriesReducedTrees(15), 2))