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A188808 T(n,k)=Number of nXk array permutations with each element remaining in its original row or its original column.

%I A188808 #7 Jul 22 2025 11:23:38
%S A188808 1,2,2,6,9,6,24,82,82,24,120,1313,2720,1313,120,720,32826,194568,
%T A188808 194568,32826,720,5040,1181737,26101232,72104097,26101232,1181737,
%U A188808 5040,40320,57905114,5919004912,57951767544,57951767544,5919004912,57905114,40320
%N A188808 T(n,k)=Number of nXk array permutations with each element remaining in its original row or its original column.
%C A188808 Table starts
%C A188808 .....1........2..........6..........24.........120........720..........5040
%C A188808 .....2........9.........82........1313.......32826....1181737......57905114
%C A188808 .....6.......82.......2720......194568....26101232.5919004912.2103543163584
%C A188808 ....24.....1313.....194568....72104097.57951767544
%C A188808 ...120....32826...26101232.57951767544
%C A188808 ...720..1181737.5919004912
%C A188808 ..5040.57905114
%C A188808 .40320
%H A188808 R. H. Hardin, <a href="/A188808/b188808.txt">Table of n, a(n) for n = 1..39</a>
%e A188808 Some solutions for 4X3
%e A188808 ..3..2.11....3..0..8....0.10..8....3..0..1....0.10.11....0..4..8....1..2..0
%e A188808 ..9..1..4....4..1..5....6..7..3....9..7.11....6..5..4....3..1..5....6..4..5
%e A188808 ..6..8..7....7..6.11....9..4..5....8.10..5....9..8..7....6..7..2....9..7..8
%e A188808 ..0.10..5...10..9..2...11..1..2....6..4..2....3..1..2...11.10..9....3.10.11
%Y A188808 Column 1 is A000142
%Y A188808 Column 2 is A006040(n+1)
%K A188808 nonn,tabl
%O A188808 1,2
%A A188808 _R. H. Hardin_ Apr 11 2011