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%I #6 Jan 25 2020 20:54:58
%S 1,3,42,1900,184550,29724388,7137090958,2393644524156,
%T 1068870144819960,613045196870306340,439190550399403297437,
%U 384354189217232125992320,403475262029493557613389128,500401167055816780694578266750,723870101627745660876118985228250
%N Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with column sums 3 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="/A331705/b331705.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = (1/n!)*Sum_{k=0..n} abs(Stirling1(n, k)) * A331645(k).
%e The a(1) = 3 matrices are:
%e [2] [1] [3]
%e [1] [2]
%Y Row n=3 of A331570.
%Y Cf. A331645, A331704.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Jan 25 2020
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