%I
%S 1,3,7,18,21,147,77,1119,2270,12273,1089,464200,4229,4148223,32941976,
%T 159812905,66153,10211281004,263321,205923976532,2439257062679,
%U 3086915165084,4199061,1526043270802300,311419986358517,4817701809545446,621665561741298232,1898993198795136209
%N Number of nonnegative integer matrices with distinct nonzero rows, total sum n each column with the same sum 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.
%F a(n) = Sum_{dn} A331572(n/d, d).
%e The a(2) = 3 matrices are:
%e [1 0] [1 1] [2]
%e [0 1]
%Y Cf. A331572.
%K nonn
%O 1,2
%A _Andrew Howroyd_, Jan 25 2020
