login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Square array T(m,n) giving the number of m X n (0,1)-matrices with pairwise distinct rows and pairwise distinct columns.
18

%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