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

0,3

Comments

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

Links

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

Formula

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

Example

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]

Crossrefs

Row n=2 of A331570.

Cf. A331644, A331705.

Sequence in context: A326324 A215084 A232058 * A275031 A094655 A327364

Adjacent sequences: A331701 A331702 A331703 * A331705 A331706 A331707

Keyword

nonn

Author

Andrew Howroyd, Jan 25 2020

Status

approved