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

0,3

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

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

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

Crossrefs

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

Sequence in context: A099953 A009324 A203236 * A103468 A192944 A306179

Adjacent sequences: A365958 A365959 A365960 * A365962 A365963 A365964

Keyword

nonn

Author

Ludovic Schwob, Sep 23 2023

Extensions

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

Status

approved