[seqfan] Re: Permutations with 2K-2 odd displacements, formula?

Neil Sloane njasloane at gmail.com
Sun Jun 2 04:22:36 CEST 2013


If you divide the rows by the first column, what you get is (conjecturally)
a triangle
whose even-numbered rows are binomial(n,k)^2, and
whose odd-numbered rows are binomial(n,k)*binomial(n-1,k)
(with some suitable re-indexing)




On Sat, Jun 1, 2013 at 6:46 PM, Ron Hardin <rhhardin at att.net> wrote:

> Can the formula for this be guessed?  The (full) row sums are n! of course.
>
> /tmp/dhp
> T(n,k)=Number of permutations of n elements with 2k-2 odd displacements
>
>
> ...........1.............0.............0............0...........0.........0......0
>
>
> ...........1.............1.............0............0...........0.........0......0
>
>
> ...........2.............4.............0............0...........0.........0......0
>
>
> ...........4............16.............4............0...........0.........0......0
>
>
> ..........12............72............36............0...........0.........0......0
>
>
> ..........36...........324...........324...........36...........0.........0......0
>
>
> .........144..........1728..........2592..........576...........0.........0......0
>
>
> .........576..........9216.........20736.........9216.........576.........0......0
>
>
> ........2880.........57600........172800.......115200.......14400.........0......0
>
>
> .......14400........360000.......1440000......1440000......360000.....14400......0
>
>
> .......86400.......2592000......12960000.....17280000.....6480000....518400......0
>
>
> ......518400......18662400.....116640000....207360000...116640000..18662400.518400
>
>
> .....3628800.....152409600....1143072000...2540160000..1905120000.457228800.......
>
>
> ....25401600....1244678400...11202105600..31116960000.31116960000.................
>
>
> ...203212800...11379916800..119489126400.398297088000.............................
>
>
> ..1625702400..104044953600.1274550681600..........................................
>
>
> .14631321600.1053455155200........................................................
>
>
> column 1 is A010551
>
> All solutions for n=4 k=2
>
> ..3....1....1....3....0....1....0....0....3....2....2....2....0....1....3....2
>
> ..1....3....3....1....2....2....1....3....2....0....0....1....2....0....0....3
>
> ..0....0....2....2....1....0....3....1....0....1....3....3....3....2....2....1
>
> ..2....2....0....0....3....3....2....2....1....3....1....0....1....3....1....0
>
>
>  rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



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