A094223 Number of binary n X n matrices with all rows (columns) distinct, up to permutation of columns (rows).

1, 2, 7, 68, 2251, 247016, 89254228, 108168781424, 451141297789858, 6625037125817801312, 348562672319990399962384, 66545827618461283102105245248, 46543235997095840080425299916917968, 120155975713532210671953821005746669185792, 1152009540439950050422144845158703009569109376384

Offset: 0

Author

Goran Kilibarda and Vladeta Jovovic, May 28 2004

Keywords

• easy
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.

Crossrefs

Main diagonal of A059584 and A059587, A060690, A088309.

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

Programs

Mathematica

a[n_] := Sum[(-1)^(n - k)*StirlingS1[n, k]*Binomial[2^k, n], {k, 0, n}]; (* or *) a[n_] := Sum[ StirlingS1[n, k]*Binomial[2^k + n - 1, n], {k, 0, n}]; Table[ a[n], {n, 0, 12}] (* Robert G. Wilson v, May 29 2004 *)

PARI

a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k+n-1, n)); \\ Michel Marcus, Dec 17 2022

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*binomial(2^k, n).

a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k+n-1, n).

Extensions

More terms from Robert G. Wilson v, May 29 2004

a(13) onwards from Andrew Howroyd, Jan 20 2024