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A331709 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.

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