%I #7 Jan 25 2020 20:55:18
%S 1,1,7,59,701,10460,190816,4098997,101523139,2847014941,89188733362,
%T 3086888531896,116982554539226,4817701229837597,214245144969388823,
%U 10231975601963484807,522307300100522413863,28379690860876378241538,1635356759307997113784404
%N Number of nonnegative integer matrices with n columns and any number of distinct nonzero rows with column sums 2 and columns in nonincreasing lexicographic order.
%C The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.
%H Andrew Howroyd, <a href="/A331709/b331709.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = (1/n!)*Sum_{k=0..n} abs(Stirling1(n, k)) * A331644(k).
%e The a(2) = 7 matrices are:
%e [1 1] [1 0] [1 0] [2 1] [2 0] [1 0] [2 2]
%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 A331572.
%Y Cf. A331644, A331710.
%K nonn
%O 0,3
%A _Andrew Howroyd_, Jan 25 2020