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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays x(i,j) with row sums sum{x(i,j), j=1..k+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing
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%I #4 Dec 08 2013 06:37:56

%S 28,98,117,286,1046,444,729,7595,10496,1588,1678,46935,202692,100400,

%T 5387,3555,254725,3297833,5346837,905636,17645,7048,1242042,46482312,

%U 241678714,133229754,7828287,56425,13215,5538026,579835701,9480398444

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays x(i,j) with row sums sum{x(i,j), j=1..k+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing

%C Table starts

%C .....28.......98........286.........729.......1678.........3555.......7048

%C ....117.....1046.......7595.......46935.....254725......1242042....5538026

%C ....444....10496.....202692.....3297833...46482312....579835701.6509469538

%C ...1588...100400....5346837...241678714.9480398444.328735086329

%C ...5387...905636..133229754.16837550455

%C ..17645..7828287.3183753917

%C ..56425.65352179

%C .177289

%H R. H. Hardin, <a href="/A233374/b233374.txt">Table of n, a(n) for n = 1..40</a>

%e Some solutions for n=2 k=4

%e ..0..0..1..0..1....2..1..1..2..0....0..2..2..0..1....1..2..0..1..1

%e ..0..1..1..2..2....0..2..0..2..2....0..2..1..2..2....0..0..2..2..1

%e ..1..2..2..2..2....1..1..2..1..2....1..0..2..2..2....1..1..1..1..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 08 2013