A181230 - OEIS

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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.

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