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%I #26 Nov 14 2023 09:22:29
%S 1,1,2,112,15109096,99550593673808010752
%N Number of equivalence classes of directed Hamiltonian cycles (or Gray codes) in the binary n-cube with one node marked.
%C Equals A066037(n)/(n!/2). See A006069, A003042, A066037 for more information.
%D D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, (to appear), section 7.2.1.1.
%H Michel Deza and Roman Shklyar, <a href="http://arxiv.org/abs/1003.4391">Enumeration of Hamiltonian Cycles in 6-cube</a>, arXiv:1003.4391v1 [There may be errors - see Haanpaa and Ostergard, 2012]
%H Harri Haanpaa and Patric R. J. Östergård, <a href="http://dx.doi.org/10.1090/S0025-5718-2013-02741-X">Counting Hamiltonian cycles in bipartite graphs</a>, Math. Comp., 88 (2014) 979-995. Final version available from http://users.tkk.fi/pat/.
%Y Cf. A006069, A003042, A066037, A159344.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, following a suggestion of _Gordon Royle_, Feb 20 2004
%E a(6) from Michel Deza, Mar 28 2010
%E a(6) corrected by Haanpaa and Östergård, 2012, who also provided a more precise definition. - _N. J. A. Sloane_, Sep 06 2012
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