A331713 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.

1, 3, 7, 18, 21, 147, 77, 1119, 2270, 12273, 1089, 464200, 4229, 4148223, 32941976, 159812905, 66153, 10211281004, 263321, 205923976532, 2439257062679, 3086915165084, 4199061, 1526043270802300, 311419986358517, 4817701809545446, 621665561741298232, 1898993198795136209

Offset: 1

Author

Andrew Howroyd, Jan 25 2020

Keywords

• nonn

Comments

The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.

Examples

			The a(2) = 3 matrices are:
  [1 0]  [1 1]  [2]
  [0 1]
		

Crossrefs

Cf. A331572.

Formula

a(n) = Sum_{d|n} A331572(n/d, d).