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A088309
Number of equivalence classes of n X n (0,1)-matrices with all rows distinct and all columns distinct.
15
1, 2, 5, 44, 1411, 159656, 62055868, 82060884560, 371036717493194, 5812014504668066528, 320454239459072905856944, 63156145369562679089674952768, 45090502574837184532027563736271152, 117910805393665959622047902193019284914432, 1139353529410754170844431642119963019965901238144
OFFSET
0,2
COMMENTS
Two such matrices are equivalent if they differ just by a permutation of the rows.
LINKS
G. Kilibarda and V. Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k, n). - Vladeta Jovovic, Nov 07 2003
a(n) = A088310(n) / n!.
EXAMPLE
a(2) = 5: 00/01, 00/10, 01/10, 01/11, 10/11.
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 *)
PROG
(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
(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
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k, n)); \\ Michel Marcus, Dec 16 2022
CROSSREFS
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.
Sequence in context: A163115 A221682 A366406 * A334252 A307147 A056680
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