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%I #14 Jul 23 2015 04:18:27
%S 1,1,14,2140,1017219,1110178602,2320017306125,8278981347401059,
%T 46556715158334549170,388779284837787599307987,
%U 4605471565794120802036550000,74633554055057890778698344509705,1606481673354648219373898238155693682,44821655543075499856527523557216582931002
%N Number of tangled chains of length k=4.
%C Tangled chains are ordered lists of k rooted binary trees with n leaves and a matching between each leaf from the i-th tree with a unique leaf from the (i+1)-st tree up to isomorphism on the binary trees. This sequence fixes k=4, and n = 1,2,3,...
%D R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.
%H S. Billey, <a href="/A258487/b258487.txt">Table of n, a(n) for n = 1..20</a>
%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)^4)/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
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