A318538 Number of n X n (0,1)-matrices with nonzero pairwise distinct rows and nonzero pairwise distinct columns.

1, 1, 6, 174, 24360, 15198120, 38415132000, 376482729702240, 14139748304132048640, 2040859528996474439366400, 1141301651605590355550899891200, 2494751188402618305982805631973248000, 21474225685319103561274021904272069843353600

Offset: 0

Author

Max Alekseyev, Aug 28 2018

Keywords

• nonn

Crossrefs

Main diagonal of A318537.

Cf. A094000, A059202.

Programs

PARI

{ A318538(n) = n! * sum(i=0, n, stirling(n+1, i+1) * binomial(2^i - 1, n) ); }

Formula

a(n) = n! * Sum_{i=0..n} Stirling1(n+1,i+1) * binomial(2^i-1,n).

a(n) = A318537(n,n).

a(n) = A094000(n) * n!.