%I #18 Mar 08 2018 18:51:05

%S 2,2,2,0,10,0,0,24,24,0,0,24,264,24,0,0,0,1608,1608,0,0,0,0,6720,

%T 33864,6720,0,0,0,0,20160,483840,483840,20160,0,0,0,0,40320,5644800,

%U 19158720,5644800,40320,0,0,0,0,40320,57415680,595506240,595506240,57415680,40320

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

%C Table starts

%C .2..2.....0...........0...............0..................0

%C .2.10....24..........24...............0..................0

%C .0.24...264........1608............6720..............20160

%C .0.24..1608.......33864..........483840............5644800

%C .0..0..6720......483840........19158720..........595506240

%C .0..0.20160.....5644800.......595506240........44680224960

%C .0..0.40320....57415680.....16388749440......2881362718080

%C .0..0.40320...518676480....418910083200....172145618789760

%C .0..0.....0..4151347200..10136835072000...9841604944066560

%C .0..0.....0.29059430400.233811422208000.546156941728204800

%H R. H. Hardin, <a href="/A181230/b181230.txt">Table of n, a(n) for n=1..180</a>

%H MathOverflow, <a href="http://mathoverflow.net/questions/158385/number-of-matrices-with-no-repeated-columns-or-rows">Number of matrices with no repeated columns or rows</a>

%F 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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Oct 10 2010