A258489 - OEIS

%I #16 Jul 24 2015 05:25:17

%S 1,1,122,474883,11168414844,989169269347359,250335000079534559375,

%T 151038989624520433840089358,191158216491241179675824199407135,

%U 461408865973380293005829125668717407727,1973397409908124305318632313047269426852165625,14104214451439837037643144221899175649593123932192274

%N Number of tangled chains of length k=6.

%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=6, 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)^6)/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