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A233062 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..k+1} nondecreasing, and column sums sum{i*x(i,j), i=1..n+1} nondecreasing.

%I A233062 #6 Jul 23 2025 07:50:20
%S A233062 7,13,16,22,47,33,34,130,161,66,50,319,723,564,132,70,755,2875,4393,
%T A233062 1933,265,95,1680,10650,30692,26819,6529,530,125,3673,36674,197625,
%U A233062 334580,162916,21904,1052,161,7751,119979,1180594,3849923,3654675,986252,72710
%N A233062 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..k+1} nondecreasing, and column sums sum{i*x(i,j), i=1..n+1} nondecreasing.
%C A233062 Table starts
%C A233062 ....7.....13........22.........34..........50..........70..........95
%C A233062 ...16.....47.......130........319.........755........1680........3673
%C A233062 ...33....161.......723.......2875.......10650.......36674......119979
%C A233062 ...66....564......4393......30692......197625.....1180594.....6637131
%C A233062 ..132...1933.....26819.....334580.....3849923....41069900...410815334
%C A233062 ..265...6529....162916....3654675....76267521..1476777204.26815913185
%C A233062 ..530..21904....986252...39886178..1522090763.53995730752
%C A233062 .1052..72710...5942365..433495407.30425555678
%C A233062 .2092.238992..35694392.4690717033
%C A233062 .4183.781279.213988742
%H A233062 R. H. Hardin, <a href="/A233062/b233062.txt">Table of n, a(n) for n = 1..84</a>
%e A233062 Some solutions for n=4 k=4
%e A233062 ..0..0..1..0..1....0..0..1..1..1....0..1..0..0..1....0..0..1..1..0
%e A233062 ..0..0..0..1..1....1..1..1..0..0....1..0..1..0..0....0..0..0..1..1
%e A233062 ..0..0..0..1..1....0..1..1..0..1....0..0..0..1..1....1..0..0..1..1
%e A233062 ..1..0..0..0..1....0..0..1..1..1....0..0..1..1..0....0..1..1..0..1
%e A233062 ..0..1..1..1..1....0..1..0..1..1....0..1..0..0..1....0..1..1..1..1
%Y A233062 Row 1 is A002623(n+1)
%K A233062 nonn,tabl
%O A233062 1,1
%A A233062 _R. H. Hardin_, Dec 03 2013