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A056876
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Number of permutations (p_1, ..., p_n) of {1,...,n} that are "balanced" in the sense that the sum of kp_k equals the sum of (n+1-k)p_k; equivalently, the expected value of kp_k is (expected value of k) times (expected value of p_k), assuming the uniform distribution.
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0
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1, 0, 0, 2, 6, 0, 184, 936, 6688, 0, 420480, 4298664, 44405142, 0, 6732621476, 92014579912, 1345077232898, 0, 349174373111790, 6179276762966832, 114913276077265202, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(4k+2)=0; also, the same sequence enumerates permutations of {0,1,...,n-1} with the stated expected value property
Also, central coefficients in the expansion of the probability generating function for the exact null distribution of Spearman's rho. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 14 2002
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REFERENCES
| Ivan Moscovich, MORE BRAINMATICS LOGIC PUZZLES, see p. 130. - from Neven Juric, Jan 21 2010.
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LINKS
| M.A. van de Wiel and A. Di Bucchianico, Fast computation of the exact null distribution of Spearman's rho and Page's L statistic ... , J. of Stat. Plan. and Inference, 92 (2001), 133-145.
M.A. van de Wiel and A. Di Bucchianico, Fast computation of the exact null distribution of Spearman's rho and Page's L statistic ... , J. of Stat. Plan. and Inference, 92 (2001), 133-145.
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EXAMPLE
| a(5)=6 because of the permutations 15432, 23451, 25314, 41352, 43215, 51234.
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CROSSREFS
| Sequence in context: A106458 A122685 A109581 * A021797 A068959 A175474
Adjacent sequences: A056873 A056874 A056875 * A056877 A056878 A056879
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KEYWORD
| hard,nonn
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AUTHOR
| D. E. Knuth, Sep 03 2000
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 14 2002
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