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A365961
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Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums.
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3
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1, 1, 4, 19, 127, 967, 9063, 94595, 1139708, 15118010, 223571836, 3597458356, 63233950081, 1197193320701, 24418765771835, 532015160784016, 12363381055074017, 304754656068754421, 7952728315095555279, 218848562411197549582, 6338152295627215890669, 192627799720153909693048
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OFFSET
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0,3
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COMMENTS
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Let f(n) = number of ordered coprime factorizations of n (A325446(n)); a(n) = sum of f(k) over all terms k in A025487 that have n factors.
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LINKS
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EXAMPLE
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The a(3) = 19 matrices:
[1 1 1]
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[1 1] [1 1] [1 1 0] [1 0 1] [0 1 1]
[1 0] [0 1] [0 0 1] [0 1 0] [1 0 0]
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[1] [1 0] [0 1] [1 0] [0 1] [1 0 0] [1 0 0] [0 1] [1 0]
[1] [1 0] [0 1] [0 1] [1 0] [0 1 0] [0 0 1] [1 0] [0 1]
[1] [0 1] [1 0] [1 0] [0 1] [0 0 1] [0 1 0] [1 0] [0 1]
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[0 1 0] [0 1 0] [0 0 1] [0 0 1]
[1 0 0] [0 0 1] [1 0 0] [0 1 0]
[0 0 1] [1 0 0] [0 1 0] [1 0 0]
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PROG
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(PARI)
R(n, k)={Vec(-1 + 1/prod(j=1, k, 1 - binomial(k, j)*x^j + O(x*x^n)))}
seq(n) = {concat([1], sum(k=1, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) ))} \\ Andrew Howroyd, Sep 23 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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