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%I #4 Dec 01 2013 17:20:39
%S 7,14,14,25,45,25,39,130,130,39,57,311,650,311,57,81,637,2715,2715,
%T 637,81,112,1235,8988,21639,8988,1235,112,151,2314,26553,133532,
%U 133532,26553,2314,151,195,4200,74515,706994,1604460,706994,74515,4200,195,247,7228
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays x(i,j) with row sums sum{j^2*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 ...7....14......25........39.........57..........81..........112.........151
%C ..14....45.....130.......311........637........1235.........2314........4200
%C ..25...130.....650......2715.......8988.......26553........74515......202293
%C ..39...311....2715.....21639.....133532......706994......3457755....16257008
%C ..57...637....8988....133532....1604460....16272765....146502363..1233883972
%C ..81..1235...26553....706994...16272765...330663907...5853344894.94722968640
%C .112..2314...74515...3457755..146502363..5853344894.206695177162
%C .151..4200..202293..16257008.1233883972.94722968640
%C .195..7228..523052..72992744.9794613332
%C .247.11846.1268666.309583532
%H R. H. Hardin, <a href="/A232877/b232877.txt">Table of n, a(n) for n = 1..96</a>
%e Some solutions for n=4 k=4
%e ..1..1..0..0..0....0..0..1..1..0....0..1..0..0..0....1..1..1..0..0
%e ..0..0..1..0..0....1..0..0..0..1....1..0..1..0..0....0..0..0..0..1
%e ..0..1..1..0..0....1..0..1..0..1....1..0..0..1..0....0..0..0..0..1
%e ..0..0..0..1..1....0..1..1..0..1....0..1..0..0..1....0..0..0..0..1
%e ..0..0..1..1..1....0..0..0..1..1....0..0..1..1..1....0..0..0..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 01 2013
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