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%I #7 Jan 25 2020 20:54:50
%S 1,1,6,46,544,7983,144970,3097825,76494540,2139610590,66898897827,
%T 2311748912745,87494097274959,3599356204576335,159917091369687135,
%U 7631292367127171222,389282192196378927707,21138914821756778420757,1217459545430430305769230
%N Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with column sums 2 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.
%H Andrew Howroyd, <a href="/A331704/b331704.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n, k) * A331644(k).
%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 Row n=2 of A331570.
%Y Cf. A331644, A331705.
%K nonn
%O 0,3
%A _Andrew Howroyd_, Jan 25 2020
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