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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 10:01 EDT 2024. Contains 371779 sequences. (Running on oeis4.)