%I
%S 1,1,41,31732,106420469,1046976648840,24085106680575625,
%T 1117767454807330938472,94308987414050519542935029,
%U 13390317159105772877158700776107,3014130596940522685213135526859317500,1025828273466214412416440210115479183065903,507888918625036626314714587415852381698509422634
%N Number of tangled chains of length k=5.
%C Tangled chains are ordered lists of k rooted binary trees with n leaves and a matching between each leaf from the ith tree with a unique leaf from the (i+1)st tree up to isomorphism on the binary trees. This sequence fixes k=5, and n = 1,2,3,...
%D R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.
%H Sara Billey, Matjaž Konvalinka, and Frederick A. Matsen IV, <a href="http://arxiv.org/abs/1507.04976">On the enumeration of tanglegrams and tangled chains</a>, arXiv:1507.04976 [math.CO], 2015.
%F t(n) = Sum_{b=(b(1),...,b(t))} Product_{i=2..t} (2(b(i)+...+b(t))1)^5)/z(b) where the sum is over all binary partitions of n and z(b) is the size of the stabilizer of a permutation of cycle type b under conjugation.
%Y Cf. A000123 (binary partitions), A258620 (tanglegrams), A258485, A258486, A258487, A258488, A258489 (tangled chains), A259114 (unordered tanglegrams).
%K nonn
%O 1,3
%A _Sara Billey_, _Matjaz Konvalinka_, and _Frederick A. Matsen IV_, May 31 2015
