A088310 Number of n X n (0,1)-matrices with all rows distinct and all columns distinct.

1, 2, 10, 264, 33864, 19158720, 44680224960, 413586858182400, 14960200449325582080, 2109063823453947981680640, 1162864344149083760773678387200, 2520991223487759548686737154649702400, 21598422878151131130336454273775859841843200, 734233037731110118818452425552296701963294284185600

Offset: 0

Author

N. J. A. Sloane, Nov 07 2003

Keywords

• nonn

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..57

Crossrefs

Cf. A088229, A088309.

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

Programs

Magma

A088310:= func< n | Factorial(n)*(&+[Binomial(2^k,n)*StirlingFirst(n,k): k in [0..n]]) >;
[A088310(n): n in [0..30]]; // G. C. Greubel, Dec 14 2022

Mathematica

Table[n!*Sum[StirlingS1[n, k]*Binomial[2^k,n], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)

SageMath

@CachedFunction
def A088310(n): return (-1)^n*factorial(n)*sum((-1)^k*binomial(2^k,n)*stirling_number1(n,k) for k in (0..n))
[A088310(n) for n in range(31)] # G. C. Greubel, Dec 14 2022

Formula

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

a(n) = Sum_{i=0..n} Sum_{j=0..n} stirling1(n, i) * stirling1(n, j) * 2^(i*j). - Max Alekseyev, Nov 07 2003

a(n) ~ 2^(n^2). - Vaclav Kotesovec, Jul 02 2016

a(n) = A181230(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