A331705 Number of nonnegative integer matrices with n distinct columns and any number of distinct nonzero rows with column sums 3 and columns in decreasing lexicographic order.

1, 3, 42, 1900, 184550, 29724388, 7137090958, 2393644524156, 1068870144819960, 613045196870306340, 439190550399403297437, 384354189217232125992320, 403475262029493557613389128, 500401167055816780694578266750, 723870101627745660876118985228250

Offset

0,2

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..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 A331570.

Cf. A331645, A331704.

Sequence in context: A218308 A195010 A333323 * A156108 A210929 A083402

Adjacent sequences: A331702 A331703 A331704 * A331706 A331707 A331708

Keyword

nonn

Author

Andrew Howroyd, Jan 25 2020

Status

approved