cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A258488 Number of tangled chains of length k=5.

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%I A258488 #14 Jul 24 2015 05:23:34
%S A258488 1,1,41,31732,106420469,1046976648840,24085106680575625,
%T A258488 1117767454807330938472,94308987414050519542935029,
%U A258488 13390317159105772877158700776107,3014130596940522685213135526859317500,1025828273466214412416440210115479183065903,507888918625036626314714587415852381698509422634
%N A258488 Number of tangled chains of length k=5.
%C A258488 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,...
%D A258488 R. Page, Tangled trees: phylogeny, cospeciation, and coevolution, The University of Chicago Press, 2002.
%H A258488 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 A258488 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 A258488 Cf. A000123 (binary partitions), A258620 (tanglegrams), A258485, A258486,  A258487, A258488, A258489 (tangled chains), A259114 (unordered tanglegrams).
%K A258488 nonn
%O A258488 1,3
%A A258488 _Sara Billey_, _Matjaz Konvalinka_, and _Frederick A. Matsen IV_, May 31 2015