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%I #17 Jul 22 2015 00:23:44
%S 1,1,5,151,9944,1196991,226435150,61992679960,23198439767669,
%T 11380100883484302,7087878538028540725,5465174495550911165171,
%U 5111311778783673593594175,5701234859347275019419890715,7477492710871626347942014991975,11393306956061559325223329489826611,19958666934810234750929365717573438949,39835206091758734935374720734513530255512,89867076346063005007676287874769844881101800,227547795689116560408812799327387232156371842150
%N Number of tangled chains of length k=3.
%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=3, 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>, (2015).
%F t(n) = Sum_{b=(b(1),...,b(t))} Product_{i=2..t} (2(b(i)+...+b(t))-1)^3)/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), A258485 (tanglegrams), A258487, A258488, A258489.
%K nonn
%O 1,3
%A _Sara Billey_, May 31 2015
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