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

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(1) = 3 matrices are:
   [2]  [1]  [3]
   [1]  [2]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100

Crossrefs

Row n=3 of A331570.

Cf. A331645, A331704.

Formula

a(n) = (1/n!)*Sum_{k=0..n} abs(Stirling1(n, k)) * A331645(k).