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.

1, 1, 7, 59, 701, 10460, 190816, 4098997, 101523139, 2847014941, 89188733362, 3086888531896, 116982554539226, 4817701229837597, 214245144969388823, 10231975601963484807, 522307300100522413863, 28379690860876378241538, 1635356759307997113784404

Offset: 0

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) = 7 matrices are:
   [1 1]  [1 0]  [1 0]  [2 1]  [2 0]  [1 0]  [2 2]
   [1 0]  [1 1]  [0 1]  [0 1]  [0 2]  [1 2]
   [0 1]  [0 1]  [1 1]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Row n=2 of A331572.

Cf. A331644, A331710.

Formula

a(n) = (1/n!)*Sum_{k=0..n} abs(Stirling1(n, k)) * A331644(k).