A088309 Number of equivalence classes of n X n (0,1)-matrices with all rows distinct and all columns distinct.

1, 2, 5, 44, 1411, 159656, 62055868, 82060884560, 371036717493194, 5812014504668066528, 320454239459072905856944, 63156145369562679089674952768, 45090502574837184532027563736271152, 117910805393665959622047902193019284914432, 1139353529410754170844431642119963019965901238144

Offset: 0

Author

N. J. A. Sloane, Nov 07 2003

Keywords

• nonn

Comments

Two such matrices are equivalent if they differ just by a permutation of the rows.

Examples

			a(2) = 5: 00/01, 00/10, 01/10, 01/11, 10/11.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..59
• G. Kilibarda and V. Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.

Crossrefs

Cf. A088229, A088310, A088616.

Main diagonal of A059084.

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

Programs

Magma

A088309:= func< n | (&+[Binomial(2^k,n)*StirlingFirst(n,k): k in [0..n]]) >;
[A088309(n): n in [0..30]]; // G. C. Greubel, Dec 15 2022

Mathematica

A088309[n_]:= A088309[n]=Sum[Binomial[2^j,n]*StirlingS1[n,j], {j,0,n}];
Table[A088309[n], {n,0,30}] (* G. C. Greubel, Dec 15 2022 *)

PARI

a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k, n)); \\ Michel Marcus, Dec 16 2022

SageMath

@CachedFunction
def A088309(n): return (-1)^n*sum((-1)^k*binomial(2^k, n)*stirling_number1(n, k) for k in (0..n))
[A088309(n) for n in range(31)] # G. C. Greubel, Dec 15 2022

Formula

a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k, n). - Vladeta Jovovic, Nov 07 2003

a(n) = A088310(n) / n!.

Extensions

Suggested by Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 06 2003

a(0)-a(5) from W. Edwin Clark, Nov 07 2003