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A088309
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Number of equivalence classes of n X n (0,1)-matrices with all rows distinct and all columns distinct.
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15
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1, 2, 5, 44, 1411, 159656, 62055868, 82060884560, 371036717493194, 5812014504668066528, 320454239459072905856944, 63156145369562679089674952768, 45090502574837184532027563736271152, 117910805393665959622047902193019284914432, 1139353529410754170844431642119963019965901238144
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OFFSET
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0,2
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COMMENTS
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Two such matrices are equivalent if they differ just by a permutation of the rows.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k, n). - Vladeta Jovovic, Nov 07 2003
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EXAMPLE
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a(2) = 5: 00/01, 00/10, 01/10, 01/11, 10/11.
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MATHEMATICA
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A088309[n_]:= A088309[n]=Sum[Binomial[2^j, n]*StirlingS1[n, j], {j, 0, n}];
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PROG
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(Magma)
A088309:= func< n | (&+[Binomial(2^k, n)*StirlingFirst(n, k): k in [0..n]]) >;
(SageMath)
@CachedFunction
def A088309(n): return (-1)^n*sum((-1)^k*binomial(2^k, n)*stirling_number1(n, k) for k in (0..n))
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k, n)); \\ Michel Marcus, Dec 16 2022
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CROSSREFS
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Binary matrices with distinct rows and columns, various versions: A059202, this sequence, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Suggested by Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 06 2003
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STATUS
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approved
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