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A233301 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^2*x(i,j), i=1..n+1} nondecreasing.

%I A233301 #6 Jul 23 2025 07:59:01
%S A233301 7,13,15,22,42,31,34,105,141,64,50,232,567,502,129,70,475,1986,3556,
%T A233301 1739,258,95,904,6292,21957,21856,5964,515,125,1632,18205,122022,
%U A233301 239330,135636,20185,1029,161,2806,48913,616439,2353493,2694620,836259,67609
%N A233301 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^2*x(i,j), i=1..n+1} nondecreasing.
%C A233301 Table starts
%C A233301 ....7.....13........22.........34..........50..........70..........95
%C A233301 ...15.....42.......105........232.........475.........904........1632
%C A233301 ...31....141.......567.......1986........6292.......18205.......48913
%C A233301 ...64....502......3556......21957......122022......616439.....2871477
%C A233301 ..129...1739.....21856.....239330.....2353493....20916337...170084407
%C A233301 ..258...5964....135636....2694620....48504411...789640245.11764401320
%C A233301 ..515..20185....836259...30257296..1007309118.30406745215
%C A233301 .1029..67609...5134856..338790472.21022231309
%C A233301 .2055.224165..31326263.3761876941
%C A233301 .4107.737347.190404404
%H A233301 R. H. Hardin, <a href="/A233301/b233301.txt">Table of n, a(n) for n = 1..84</a>
%e A233301 Some solutions for n=4 k=4
%e A233301 ..0..1..0..0..1....0..1..1..0..0....0..0..0..0..0....1..0..0..0..1
%e A233301 ..0..0..1..1..1....0..0..1..0..1....1..0..0..0..1....0..1..0..1..0
%e A233301 ..1..0..0..1..1....1..1..0..0..0....0..0..0..1..1....0..0..1..1..0
%e A233301 ..0..1..1..1..1....0..0..0..1..1....0..1..1..0..0....0..0..1..0..1
%e A233301 ..0..1..1..1..1....0..0..1..1..1....0..0..0..1..1....0..0..0..1..1
%Y A233301 Row 1 is A002623(n+1)
%K A233301 nonn,tabl
%O A233301 1,1
%A A233301 _R. H. Hardin_, Dec 07 2013