%I #5 Mar 31 2012 12:36:57
%S 1212,27966,27966,557544,4859580,557544,9592248,729677481,729677481,
%T 9592248,146861704,85151157995,949250483640,85151157995,146861704,
%U 2050339423,8115230716866,931767180207600,931767180207600,8115230716866
%N T(n,k)=Number of (n+1)X(k+1) 0..7 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing
%C Table starts
%C .........1212.............27966................557544.................9592248
%C ........27966...........4859580.............729677481.............85151157995
%C .......557544.........729677481..........949250483640.........931767180207600
%C ......9592248.......85151157995.......931767180207600.....7676075878291358313
%C ....146861704.....8115230716866....726872783930414289.49640621147968317363235
%C ...2050339423...656137171037648.471365844803377449537
%C ..26569429480.46216860954254233
%C .323824032048
%H R. H. Hardin, <a href="/A203661/b203661.txt">Table of n, a(n) for n = 1..39</a>
%e Some solutions for n=5 k=3
%e ..5..2..7..3....0..0..3..0....3..0..5..3....4..4..7..2....3..6..2..5
%e ..0..7..3..7....2..4..4..7....0..6..4..6....4..5..2..7....6..3..7..4
%e ..1..7..7..3....4..3..7..4....1..5..5..5....5..4..7..3....2..7..4..7
%e ..7..2..0..7....4..4..0..5....3..3..7..6....2..7..4..6....2..7..4..7
%e ..3..6..4..4....5..4..1..7....6..2..6..5....7..3..6..2....2..7..4..7
%e ..2..7..3..5....2..7..3..0....5..5..2..2....4..6..3..5....2..7..4..7
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 04 2012
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