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

%I A339234 #8 Jan 02 2021 04:14:00
%S A339234 1,1,5,51,757,16416,461231,16021550,662197510,31749450007,
%T A339234 1732478051823,106025572201434,7192665669790893,535756912504764218,
%U A339234 43471544417828923777,3816784803681841133512,360546156617986177328681,36462349359125513109697520,3930704977357944446111295571
%N A339234 Number of series-reduced tanglegrams with n unlabeled leaves.
%C A339234 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.
%e A339234 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)
%e A339234            A             A
%e A339234           /  \          /  \
%e A339234          /   / \       /   / \
%e A339234         o   o   o     o   o   o
%e A339234          \  |  /       \ /   /
%e A339234           \ | /          \  /
%e A339234             B              B
%o A339234 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A339234 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)}
%o A339234 NumUnlabeledObjsSeq(sCartPower(seriesReducedTrees(15), 2))
%Y A339234 Cf. A000669 (series-reduced trees), A258620 (binary tanglegrams), A339645.
%K A339234 nonn
%O A339234 1,3
%A A339234 _Andrew Howroyd_, Jan 01 2021