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A094223
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Number of binary n X n matrices with all rows (columns) distinct, up to permutation of columns (rows).
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13
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1, 2, 7, 68, 2251, 247016, 89254228, 108168781424, 451141297789858, 6625037125817801312, 348562672319990399962384, 66545827618461283102105245248, 46543235997095840080425299916917968, 120155975713532210671953821005746669185792, 1152009540439950050422144845158703009569109376384
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*binomial(2^k, n).
a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k+n-1, n).
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MATHEMATICA
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a[n_] := Sum[(-1)^(n - k)*StirlingS1[n, k]*Binomial[2^k, n], {k, 0, n}]; (* or *) a[n_] := Sum[ StirlingS1[n, k]*Binomial[2^k + n - 1, n], {k, 0, n}]; Table[ a[n], {n, 0, 12}] (* Robert G. Wilson v, May 29 2004 *)
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PROG
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(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k+n-1, n)); \\ Michel Marcus, Dec 17 2022
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CROSSREFS
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Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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