cp's OEIS Frontend

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

%I A365961 #18 Jan 17 2024 14:28:12
%S A365961 1,1,4,19,127,967,9063,94595,1139708,15118010,223571836,3597458356,
%T A365961 63233950081,1197193320701,24418765771835,532015160784016,
%U A365961 12363381055074017,304754656068754421,7952728315095555279,218848562411197549582,6338152295627215890669,192627799720153909693048
%N A365961 Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums.
%C A365961 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.
%H A365961 Andrew Howroyd, <a href="/A365961/b365961.txt">Table of n, a(n) for n = 0..200</a>
%e A365961 The a(3) = 19 matrices:
%e A365961   [1 1 1]
%e A365961 .
%e A365961   [1 1] [1 1] [1 1 0] [1 0 1] [0 1 1]
%e A365961   [1 0] [0 1] [0 0 1] [0 1 0] [1 0 0]
%e A365961 .
%e A365961   [1] [1 0] [0 1] [1 0] [0 1] [1 0 0] [1 0 0] [0 1] [1 0]
%e A365961   [1] [1 0] [0 1] [0 1] [1 0] [0 1 0] [0 0 1] [1 0] [0 1]
%e A365961   [1] [0 1] [1 0] [1 0] [0 1] [0 0 1] [0 1 0] [1 0] [0 1]
%e A365961 .
%e A365961   [0 1 0] [0 1 0] [0 0 1] [0 0 1]
%e A365961   [1 0 0] [0 0 1] [1 0 0] [0 1 0]
%e A365961   [0 0 1] [1 0 0] [0 1 0] [1 0 0]
%o A365961 (PARI)
%o A365961 R(n,k)={Vec(-1 + 1/prod(j=1, k, 1 - binomial(k,j)*x^j + O(x*x^n)))}
%o A365961 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
%Y A365961 Cf. A068313, A035341, A321735, A101370, A321733, A104602, A116540.
%K A365961 nonn
%O A365961 0,3
%A A365961 _Ludovic Schwob_, Sep 23 2023
%E A365961 Terms a(13) and beyond from _Andrew Howroyd_, Sep 23 2023