A331710 Number of nonnegative integer matrices with n columns and any number of distinct nonzero rows with column sums 3 and columns in nonincreasing lexicographic order.

1, 3, 45, 1987, 190379, 30474159, 7287577611, 2436916655479, 1085776582252197, 621663581843731535, 444746638465623906738, 388773810523972862494769, 407727415097448880517583006, 505268334502886263575349570013, 730406898110019766652845079212010

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(1) = 3 matrices are:
  [2]  [1]  [3]
  [1]  [2]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100

Crossrefs

Row n=3 of A331572.

Cf. A331645, A331709.

Formula

a(n) = (1/n!)*Sum_{k=0..n} abs(Stirling1(n, k)) * A331645(k).