A331316 Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with each column sum being 2 and rows in decreasing lexicographic order.

1, 1, 4, 27, 266, 3599, 62941, 1372117, 36248765, 1135864306, 41501271477, 1743624004536, 83268125043937, 4476101995389591, 268589319338401864, 17860954789864760357, 1307982591075162739660, 104895999816356419875935, 9166919404389461922512723

Offset

0,3

Comments

The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows.

Links

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

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A094574(k).

Example

The a(2) = 4 matrices are:
   [2 1]   [2 0]   [1 2]   [1 1]
   [0 1]   [0 2]   [1 0]   [1 0]
                           [0 1]

Crossrefs

Row n=2 of A331160.

Cf. A094574.

Sequence in context: A218653 A359461 A121353 * A353233 A265270 A161633

Adjacent sequences: A331313 A331314 A331315 * A331317 A331318 A331319

Keyword

nonn

Author

Andrew Howroyd, Jan 13 2020

Status

approved