A181230 Square array T(m,n) giving the number of m X n (0,1)-matrices with pairwise distinct rows and pairwise distinct columns.

2, 2, 2, 0, 10, 0, 0, 24, 24, 0, 0, 24, 264, 24, 0, 0, 0, 1608, 1608, 0, 0, 0, 0, 6720, 33864, 6720, 0, 0, 0, 0, 20160, 483840, 483840, 20160, 0, 0, 0, 0, 40320, 5644800, 19158720, 5644800, 40320, 0, 0, 0, 0, 40320, 57415680, 595506240, 595506240, 57415680, 40320

Offset: 1

Author

R. H. Hardin, Oct 10 2010

Keywords

• nonn
• tabl

Examples

			Table starts
.2..2.....0...........0...............0..................0
.2.10....24..........24...............0..................0
.0.24...264........1608............6720..............20160
.0.24..1608.......33864..........483840............5644800
.0..0..6720......483840........19158720..........595506240
.0..0.20160.....5644800.......595506240........44680224960
.0..0.40320....57415680.....16388749440......2881362718080
.0..0.40320...518676480....418910083200....172145618789760
.0..0.....0..4151347200..10136835072000...9841604944066560
.0..0.....0.29059430400.233811422208000.546156941728204800
		

Links

• R. H. Hardin, Table of n, a(n) for n=1..180
• MathOverflow, Number of matrices with no repeated columns or rows

Crossrefs

Cf. A088310 (diagonal), A181231, A181232, A181233 (subdiagonals).

Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763

Formula

T(m,n) = Sum_{i=0..n} Sum_{j=0..m} stirling1(n,i) * stirling1(m,j) * 2^(i*j) = n! * Sum_{j=0..m} stirling1(m,j) * binomial(2^j,n) = m! * Sum_{i=0..n} stirling1(n,i) * binomial(2^i,m). - Max Alekseyev, Jun 18 2016

T(m,n) = A059084(m,n) * n!.