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

0,3

Comments

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

Links

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

Formula

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

Example

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]

Crossrefs

Row n=2 of A331572.

Cf. A331644, A331710.

Sequence in context: A192458 A203237 A099347 * A203174 A183260 A285227

Adjacent sequences: A331706 A331707 A331708 * A331710 A331711 A331712

Keyword

nonn

Author

Andrew Howroyd, Jan 25 2020

Status

approved