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 A181230 Square array T(m,n) giving the number of m X n (0,1)-matrices with pairwise distinct rows and pairwise distinct columns. 18
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 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!. 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 Sequence in context: A298819 A307520 A265648 * A262372 A292520 A131079 Adjacent sequences:  A181227 A181228 A181229 * A181231 A181232 A181233 KEYWORD nonn,tabl AUTHOR R. H. Hardin Oct 10 2010 STATUS approved

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)