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A221438 T(n,k) is the number of n X k 1..(max n,k) arrays with each row and column having unrepeated values.

%I A221438 #7 Feb 20 2025 19:34:43
%S A221438 1,2,2,6,2,6,24,12,12,24,120,216,12,216,120,720,5280,576,576,5280,720,
%T A221438 5040,190800,66240,576,66240,190800,5040,40320,9344160,15321600,
%U A221438 161280,161280,15321600,9344160,40320,362880,598066560,5411750400,283046400
%N A221438 T(n,k) is the number of n X k 1..(max n,k) arrays with each row and column having unrepeated values.
%C A221438 Table starts:
%C A221438 ....1.......2..........6...........24............120............720
%C A221438 ....2.......2.........12..........216...........5280.........190800
%C A221438 ....6......12.........12..........576..........66240.......15321600
%C A221438 ...24.....216........576..........576.........161280......283046400
%C A221438 ..120....5280......66240.......161280.........161280......812851200
%C A221438 ..720..190800...15321600....283046400......812851200......812851200
%C A221438 .5040.9344160.5411750400.782137036800.20449013760000.61479419904000
%H A221438 R. H. Hardin, <a href="/A221438/b221438.txt">Table of n, a(n) for n = 1..83</a>
%e A221438 Some solutions for n=3 and k=4:
%e A221438 ..4..1..3..2....3..1..4..2....1..2..4..3....3..4..2..1....2..3..4..1
%e A221438 ..2..3..4..1....1..3..2..4....3..4..1..2....1..2..3..4....1..4..3..2
%e A221438 ..1..4..2..3....2..4..3..1....2..1..3..4....2..1..4..3....3..2..1..4
%Y A221438 Diagonal is A002860.
%Y A221438 Column 1 is A000142.
%Y A221438 Column 2 is A082491.
%K A221438 nonn,tabl
%O A221438 1,2
%A A221438 _R. H. Hardin_, Jan 16 2013