login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056876 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. 3
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; text; internal format)
OFFSET

1,4

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

REFERENCES

Ivan Moscovich, More Brainmatics Logic Puzzles, see p. 130. - from Neven Juric, Jan 21 2010.

LINKS

Table of n, a(n) for n=1..22.

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. [broken link]

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 for samples with and without ties, Memorandum COSOR 98-17, 1998, Eindhoven University of Technology

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.

EXAMPLE

a(5)=6 because of the permutations 15432, 23451, 25314, 41352, 43215, 51234.

CROSSREFS

Sequence in context: A293016 A122685 A109581 * A255484 A021797 A068959

Adjacent sequences:  A056873 A056874 A056875 * A056877 A056878 A056879

KEYWORD

hard,nonn

AUTHOR

Don Knuth, Sep 03 2000

EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 14 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 13:09 EST 2019. Contains 319271 sequences. (Running on oeis4.)