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

Author

Andrew Howroyd, Jan 13 2020

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Row n=2 of A331160.

Cf. A094574.

Formula

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