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T(n,k)=Number of nXk arrays of permutations of 0..n*k-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 7.
5

%I #5 Nov 25 2015 07:48:42

%S 1,1,1,2,3,1,4,15,6,1,12,130,170,23,1,36,1944,9656,3089,112,1,144,

%T 40188,1369408,1685728,106568,561,1,576,1149120,275062400,1816673024,

%U 410210112,4676432,3519,2,2880,49148112,89203565824

%N T(n,k)=Number of nXk arrays of permutations of 0..n*k-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 7.

%C Table starts

%C .1....1.......2.........4.........12........36.........144......576.2880

%C .1....3......15.......130.......1944.....40188.....1149120.49148112

%C .1....6.....170......9656....1369408.275062400.89203565824

%C .1...23....3089...1685728.1816673024

%C .1..112..106568.410210112

%C .1..561.4676432

%C .1.3519

%C .2

%e Some solutions for n=3 k=4

%e ..0..1..7..9....0..9..1..7....0..1..9..7....8..7..1..9....9..7..1..3

%e ..4..8..2.10....8..2..3.11....2..4.10..8....2..0..4.10...10..0..2..4

%e ..6.11..3..5....4..6.10..5....6..5..3.11....6..3..5.11....6..8..5.11

%Y Row 1 is A111942(n+1).

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Nov 25 2015