A226288 T(n,k) = [n/2]!*[(n+1)/2]!*C([n/2],k-1)*C([(n+1)/2],k-1).

1, 0, 1, 0, 1, 2, 0, 0, 4, 4, 0, 0, 0, 16, 12, 0, 0, 0, 4, 72, 36, 0, 0, 0, 0, 36, 324, 144, 0, 0, 0, 0, 0, 324, 1728, 576, 0, 0, 0, 0, 0, 36, 2592, 9216, 2880, 0, 0, 0, 0, 0, 0, 576, 20736, 57600, 14400, 0, 0, 0, 0, 0, 0, 0, 9216, 172800, 360000, 86400, 0, 0, 0, 0, 0, 0, 0, 576, 115200, 1440000, 2592000, 518400

Offset: 1

Author

R. H. Hardin, connection of formula with combinatoric problem via N. J. A. Sloane in the Sequence Fans Mailing List, Jun 02 2013

Keywords

• nonn
• tabl

Comments

T(n,k)=Number of permutations of n elements with 2k-2 odd displacements

Table starts:

.........1...........0............0............0............0............0

.........1...........1............0............0............0............0

.........2...........4............0............0............0............0

.........4..........16............4............0............0............0

........12..........72...........36............0............0............0

........36.........324..........324...........36............0............0

.......144........1728.........2592..........576............0............0

.......576........9216........20736.........9216..........576............0

......2880.......57600.......172800.......115200........14400............0

.....14400......360000......1440000......1440000.......360000........14400

.....86400.....2592000.....12960000.....17280000......6480000.......518400

....518400....18662400....116640000....207360000....116640000.....18662400

...3628800...152409600...1143072000...2540160000...1905120000....457228800

..25401600..1244678400..11202105600..31116960000..31116960000..11202105600

.203212800.11379916800.119489126400.398297088000.497871360000.238978252800

Links

• R. H. Hardin, Table of n, a(n) for n = 1..10000

Crossrefs

Column 1 is A010551.

Columns 2-7 are: A226282-A226287.

Cf. A145891 (another version as irregular triangle)

Programs

Mathematica

T[n_,k_]:=(Floor[n/2])!*(Floor[(n+1)/2])!*Binomial[Floor[n/2],k-1]*Binomial[Floor[(n+1)/2],k-1]; Table[Reverse[Table[T[n-k+1,k],{k,n}]],{n,12}]//Flatten (* Stefano Spezia, Jul 12 2024 *)