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%I #5 Jan 25 2020 20:55:25
%S 1,2,4,10,6,100,14,832,1928,9280,66,409928,134,3138847,32173339,
%T 134531629,618,9353244335,1178,183394485615,2395983801112,
%U 2311773448717,4758,1479147860804022,311353753955807,3599356750729620,613047176698674761,1842753685676233794,30462
%N Number of nonnegative integer matrices with distinct nonzero rows, total sum n, distinct columns with equals sums and columns in decreasing lexicographic order.
%C The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.
%F a(n) = Sum_{d|n} A331570(n/d, d).
%e The a(4) = 10 matrices are:
%e [1 0 0 0] [1 1] [1 0] [1 0]
%e [0 1 0 0] [1 0] [1 1] [0 1]
%e [0 0 1 0] [0 1] [0 1] [1 1]
%e [0 0 0 1]
%e .
%e [2 1] [2 0] [1 0] [3] [1] [4]
%e [0 1] [0 2] [1 2] [1] [3]
%Y Cf. A331570.
%K nonn
%O 1,2
%A _Andrew Howroyd_, Jan 25 2020
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