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A258488
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Number of tangled chains of length k=5.
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8
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1, 1, 41, 31732, 106420469, 1046976648840, 24085106680575625, 1117767454807330938472, 94308987414050519542935029, 13390317159105772877158700776107, 3014130596940522685213135526859317500, 1025828273466214412416440210115479183065903, 507888918625036626314714587415852381698509422634
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OFFSET
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1,3
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COMMENTS
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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=5, and n = 1,2,3,...
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REFERENCES
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R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.
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LINKS
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FORMULA
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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