A331704 Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with column sums 2 and columns in decreasing lexicographic order.

1, 1, 6, 46, 544, 7983, 144970, 3097825, 76494540, 2139610590, 66898897827, 2311748912745, 87494097274959, 3599356204576335, 159917091369687135, 7631292367127171222, 389282192196378927707, 21138914821756778420757, 1217459545430430305769230

Offset: 0

Author

Andrew Howroyd, Jan 25 2020

Keywords

• nonn

Comments

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

Examples

			The a(2) = 6 matrices are:
   [1 1]  [1 0]  [1 0]  [2 1]  [2 0]  [1 0]
   [1 0]  [1 1]  [0 1]  [0 1]  [0 2]  [1 2]
   [0 1]  [0 1]  [1 1]
		

Links

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

Crossrefs

Row n=2 of A331570.

Cf. A331644, A331705.

Formula

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