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A331709
Number of nonnegative integer matrices with n columns and any number of distinct nonzero rows with column sums 2 and columns in nonincreasing lexicographic order.
3
1, 1, 7, 59, 701, 10460, 190816, 4098997, 101523139, 2847014941, 89188733362, 3086888531896, 116982554539226, 4817701229837597, 214245144969388823, 10231975601963484807, 522307300100522413863, 28379690860876378241538, 1635356759307997113784404
OFFSET
0,3
COMMENTS
The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.
LINKS
FORMULA
a(n) = (1/n!)*Sum_{k=0..n} abs(Stirling1(n, k)) * A331644(k).
EXAMPLE
The a(2) = 7 matrices are:
[1 1] [1 0] [1 0] [2 1] [2 0] [1 0] [2 2]
[1 0] [1 1] [0 1] [0 1] [0 2] [1 2]
[0 1] [0 1] [1 1]
CROSSREFS
Row n=2 of A331572.
Sequence in context: A192458 A203237 A099347 * A203174 A183260 A285227
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 25 2020
STATUS
approved