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

[Neil Sloane]

In fact, after dividing by the entries at the start of the rows,
we seem to get A124428


On Sat, Jun 1, 2013 at 10:22 PM, Neil Sloane <njasloane at gmail.com> wrote:

> 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
>
>


-- 
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