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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.
3
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
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.
Sequence in context: A218308 A195010 A333323 * A156108 A210929 A083402
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 25 2020
STATUS
approved