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A094000
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Number of n X n (0,1)-matrices with no zero rows or columns and with all rows distinct and all columns distinct, up to permutation of rows.
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16
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1, 1, 3, 29, 1015, 126651, 53354350, 74698954306, 350688201987402, 5624061753186933530, 314512139441575825493524, 62498777166571927258267336860, 44831219113504221199415663547412096
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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G. Kilibarda and V. Jovovic, "Enumeration of some classes of T_0-hypergraphs", in
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n+1} Stirling1(n+1, k)*binomial(2^(k-1)-1, n).
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MATHEMATICA
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f[n_] := Sum[ StirlingS1[n + 1, k] Binomial[2^(k - 1) - 1, n], {k, 0, n + 1}]; Table[ f[n], {n, 0, 12}] (* Robert G. Wilson v, Jun 01 2004 *)
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PROG
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(PARI) a(n) = sum(k=0, n+1, stirling(n+1, k, 1)*binomial(2^(k-1)-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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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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