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%I #5 May 23 2023 12:05:17
%S 13,42,141,502,1739,5964,20185,67609,224165,737347,2407911,7814616,
%T 25223004,81015137,259099567,825507109,2621224089,8298060296,
%U 26197890927,82506334112,259260476024
%N Number of (n+1) X (2+1) 0..1 arrays x(i,j) with row sums Sum_{j=1..2+1} x(i,j) nondecreasing, and column sums Sum_{i=1..n+1} i^2*x(i,j) nondecreasing.
%C Column 2 of A233301.
%e Some solutions for n=5
%e ..0..1..0....1..1..0....0..0..0....0..0..0....0..0..1....0..0..0....1..0..0
%e ..1..1..0....1..1..0....0..0..0....0..1..0....0..1..0....0..0..0....0..0..1
%e ..0..1..1....1..0..1....1..0..0....0..0..1....0..1..0....0..0..0....1..1..0
%e ..0..1..1....0..1..1....0..1..0....0..0..1....0..0..1....0..0..0....1..1..0
%e ..1..0..1....0..1..1....0..0..1....0..0..1....1..0..0....0..0..1....1..0..1
%e ..0..1..1....1..1..1....1..1..1....1..1..1....0..1..1....0..1..1....0..1..1
%Y Cf. A233301.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 07 2013
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