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A331704
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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.
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3
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1, 1, 6, 46, 544, 7983, 144970, 3097825, 76494540, 2139610590, 66898897827, 2311748912745, 87494097274959, 3599356204576335, 159917091369687135, 7631292367127171222, 389282192196378927707, 21138914821756778420757, 1217459545430430305769230
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OFFSET
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0,3
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COMMENTS
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The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.
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LINKS
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FORMULA
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a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n, k) * A331644(k).
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EXAMPLE
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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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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