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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.
3
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
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.
Sequence in context: A326324 A215084 A232058 * A275031 A094655 A327364
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 25 2020
STATUS
approved