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A047707
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Number of monotone Boolean functions of n variables with 3 mincuts. Also Sperner systems with 3 blocks.
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37
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0, 0, 0, 2, 64, 1090, 14000, 153762, 1533504, 14356610, 128722000, 1119607522, 9528462944, 79817940930, 660876543600, 5424917141282, 44246078560384, 359144709794050, 2904688464582800, 23429048035827042, 188593339362097824
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OFFSET
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0,4
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COMMENTS
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The paper by G. Kilibarda, Enumeration of certain classes of antichains, Publications de l'Institut Mathematique, Nouvelle série, 97 (111) (2015), mentions many sequences, but since only very condensed formulas are given, it is hard to match them with entries in the OEIS. It would be nice to add this reference to all the sequences that it mentions. - N. J. A. Sloane, Jan 01 2016
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 292, #8, s(n,3).
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LINKS
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FORMULA
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a(n) = (2^n)*(2^n - 1)*(2^n - 2)/6 - (6^n - 5^n - 4^n + 3^n).
G.f.: -2*x^3*(36*x^2-4*x-1)/((2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Jul 31 2012
a(n) = Binomial(2^n,3) - (6^n - 5^n - 4^n + 3^n). - Ross La Haye, Jan 26 2016
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MATHEMATICA
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Table[Binomial[2^n, 3] - (6^n - 5^n - 4^n + 3^n), {n, 20}] (* or *)
CoefficientList[Series[-2 x^3 (36 x^2 - 4 x - 1)/((2 x - 1) (3 x - 1) (4 x - 1) (5 x - 1) (6 x - 1) (8 x - 1)), {x, 0, 20}], x] (* Michael De Vlieger, Jan 26 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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