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Number of nonnegative integer matrices with pairwise distinct nonzero rows, the total sum of elements equal n, the same sum of elements in each column, and the columns coming in nonincreasing lexicographic order.
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%I #8 Sep 11 2024 23:00:14

%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 pairwise distinct nonzero rows, the total sum of elements equal n, the same sum of elements in each column, and the columns coming 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_{d|n} 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