A365961 Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums.

1, 1, 4, 19, 127, 967, 9063, 94595, 1139708, 15118010, 223571836, 3597458356, 63233950081, 1197193320701, 24418765771835, 532015160784016, 12363381055074017, 304754656068754421, 7952728315095555279, 218848562411197549582, 6338152295627215890669, 192627799720153909693048

Offset: 0

Author

Ludovic Schwob, Sep 23 2023

Keywords

• nonn

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.

Examples

			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]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A068313, A035341, A321735, A101370, A321733, A104602, A116540.

Programs

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

Extensions

Terms a(13) and beyond from Andrew Howroyd, Sep 23 2023