A181204 T(n,k) = 0!*1!*2!*...*(k-1)! *(n*k)! *k*(k-1)*n*(n-1) / 2*n!*(n+1)!*...*(n+k-1)!

0, 0, 0, 0, 4, 0, 0, 30, 30, 0, 0, 168, 756, 168, 0, 0, 840, 16632, 16632, 840, 0, 0, 3960, 360360, 1729728, 360360, 3960, 0, 0, 18018, 7876440, 199536480, 199536480, 7876440, 18018, 0, 0, 80080, 174594420, 25241364720, 140229804000, 25241364720

Offset

1,5

Comments

(Empricial) T(n,k)=Number of nXk matrices containing a defective permutation of 1..n*k in strictly increasing order rowwise and columnwise, with one permutation value omitted and one repeated (see example)

Formula is n*(n-1)*k*(k-1)/2 times n-th k-dimensional Catalan number

Table starts

.0.......0.............0....................0...........................0

.0.......4............30..................168.........................840

.0......30...........756................16632......................360360

.0.....168.........16632..............1729728...................199536480

.0.....840........360360............199536480................140229804000

.0....3960.......7876440..........25241364720.............118949931243000

.0...18018.....174594420........3445446284280..........117015012361447200

.0...80080....3926434512......500598983364480.......129624266420759510400

.0..350064...89492111280....76591644454765440....158211402715245473193600

.0.1511640.2064420294300.12237255920840932800.209298196564031904834960000

Links

R. H. Hardin, Table of n, a(n) for n=1..1000

Example

Some solutions for 4X2
..2..4....1..4....1..3....1..3....2..5....1..3....1..3....2..4....1..2....1..3
..3..5....2..5....3..6....2..4....3..6....2..4....2..4....3..6....2..4....2..4
..5..7....6..7....4..7....4..6....4..7....4..5....4..7....5..7....3..5....4..7
..6..8....7..8....5..8....5..8....5..8....7..8....5..8....6..8....6..8....6..8

Crossrefs

Column 2 is twice A002740(n+1)

Cf. A060854 for permutation without defect.

Sequence in context: A196302 A307186 A060784 * A191417 A307050 A223179

Adjacent sequences: A181201 A181202 A181203 * A181205 A181206 A181207

Keyword

nonn,tabl

Author

R. H. Hardin Oct 10 2010

Status

approved