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%I #5 Jan 25 2020 20:55:05
%S 0,1,6,42,268,1239,7278,40828,201084,1044693,5171998,24532674,
%T 116470596,546141979,2505755010,11318525016,50046272884,219637249269,
%U 944072863998,4029243437158,16977344149608,70370874102975,289702060529770,1177283903977008,4740700176809748
%N Number of nonnegative integer matrices with 2 distinct columns and any number of distinct nonzero rows with column sums n 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) = (A331646(n) - A032020(n)) / 2.
%e The a(2) = 6 matrices are:
%e [1 1] [1 0] [1 0] [2 1] [2 0] [1 0]
%e [1 0] [1 1] [0 1] [0 1] [0 2] [1 2]
%e [0 1] [0 1] [1 1]
%Y Column k=2 of A331570.
%Y Cf. A032020, A331646, A331707.
%K nonn
%O 0,3
%A _Andrew Howroyd_, Jan 25 2020
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