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A006967
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Number of graceful permutations of length n.
(Formerly M3229)
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10
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1, 1, 2, 4, 4, 8, 24, 32, 40, 120, 296, 648, 1328, 3200, 9912, 25592, 55920, 143192, 510696, 1451296, 3497344, 10451824, 38570704, 118914992, 315235872, 1014824752, 3963684496, 13166130152, 37846301904, 130507967088, 533318630936, 1884550215976, 5800121391936
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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Also the number of graceful labelings of the path graph P_n. - Eric W. Weisstein, Mar 31 2020
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
H. S. Wilf and N. Yoshimura, Ranking rooted trees and a graceful application, in Discrete Algorithms and Complexity (Proceedings of the Japan-US joint seminar, 1986, Kyoto, Japan), edited by D. Johnson, T. Nishizeki, A. Nozaki and H. S. Wilf, Academic Press, NY, 1987, pp. 341-350.
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LINKS
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FORMULA
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PROG
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(CWEB) programs by Don Knuth: see links above
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CROSSREFS
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KEYWORD
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nonn,nice,hard
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AUTHOR
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EXTENSIONS
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n=2 term corrected June 1996
More terms from Michal Adamaszek (aszek(AT)mimuw.edu.pl), Aug 22 2006
a(41)=1032009647743958000 from Don Knuth, Sep 10 2020
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STATUS
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approved
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