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

0,2

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..100

Formula

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

Example

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

Crossrefs

Row n=3 of A331572.

Cf. A331645, A331709.

Sequence in context: A012780 A072503 A154242 * A283698 A163002 A117253

Adjacent sequences: A331707 A331708 A331709 * A331711 A331712 A331713

Keyword

nonn

Author

Andrew Howroyd, Jan 25 2020

Status

approved