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
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
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!.