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A005271
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Number of perfect matchings in n-cube.
(Formerly M1955)
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6
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OFFSET
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1,2
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COMMENTS
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The matchings contain 2^n / 2 = 2^(n-1) edges.
a(6) was first found by D. H. Wiedemann, unpublished (see Clark et al., Skupien).
Also the number of minimum edge covers and minimum clique coverings in the n-hypercube graph. - Eric W. Weisstein, Dec 24 2017
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REFERENCES
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L. H. Clark, J. C. George and T. D. Porter, On the number of 1-factors in the n-cube, Congress. Numer., 127 (1997), 67-69.
J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 18).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Eric Weisstein's World of Mathematics, Matching
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EXAMPLE
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G.f. = x + 2*x^2 + 9*x^3 + 272*x^4 + 589185*x^5 + 16332454526976*x^6 + ...
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CROSSREFS
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KEYWORD
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nonn,hard,more,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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