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URL: https://oeis.org/A365961

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A365961
Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums.
3
1, 1, 4, 19, 127, 967, 9063, 94595, 1139708, 15118010, 223571836, 3597458356, 63233950081, 1197193320701, 24418765771835, 532015160784016, 12363381055074017, 304754656068754421, 7952728315095555279, 218848562411197549582, 6338152295627215890669, 192627799720153909693048
OFFSET
0,3
COMMENTS
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.
LINKS
EXAMPLE
The a(3) = 19 matrices:
[1 1 1]
.
[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]
.
[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]
.
[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]
PROG
(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
KEYWORD
nonn
AUTHOR
Ludovic Schwob, Sep 23 2023
EXTENSIONS
Terms a(13) and beyond from Andrew Howroyd, Sep 23 2023
STATUS
approved