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A088310 Number of n X n (0,1)-matrices with all rows distinct and all columns distinct. 17
1, 2, 10, 264, 33864, 19158720, 44680224960, 413586858182400, 14960200449325582080, 2109063823453947981680640, 1162864344149083760773678387200, 2520991223487759548686737154649702400, 21598422878151131130336454273775859841843200, 734233037731110118818452425552296701963294284185600 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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).
EXAMPLE
a(2) = 10: 00/01, 00/10, 01/00, 01/10, 01/11, 10/00, 10/01, 10/11, 11/01, 11/10.
MATHEMATICA
Table[n!*Sum[StirlingS1[n, k]*Binomial[2^k, n], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
PROG
(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
(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
CROSSREFS
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: A360945 A308756 A225371 * A134473 A005154 A074056
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 07 2003
EXTENSIONS
Suggested by Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 06 2003
a(0)-a(5) from W. Edwin Clark, Nov 07 2003
STATUS
approved

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Last modified May 18 16:47 EDT 2024. Contains 372664 sequences. (Running on oeis4.)