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A003468
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Number of minimal 3-covers of a labeled n-set.
(Formerly M5125)
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6
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1, 22, 305, 3410, 33621, 305382, 2619625, 21554170, 171870941, 1337764142, 10216988145, 76862115330, 571247591461, 4203844925302, 30687029023865, 222518183370890, 1604626924403181, 11518132293452862
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OFFSET
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3,2
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COMMENTS
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This is also the fourth column of the Sheffer triangle A143496 (4-restricted Stirling2 numbers). See the e.g.f. given below. See also the Sheffer comments in A193685. - Wolfdieter Lang, Oct 08 2011
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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E.g.f.: (exp(4*x)*(exp(x) - 1)^3)/6. More generally, e.g.f. for number of minimal m-covers of a labeled n-set is (exp((2^m - m - 1)*x)*(exp(x) - 1)^m)/m!. - Vladeta Jovovic, May 09 2004
If we define f(m, j, x) = sum(binomial(m, k)*stirling2(k, j)*x^(m - k),k = j .. m) then a(n) = f(n, 3, 4), (n >= 3). - Milan Janjic, Apr 26 2009
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MAPLE
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MATHEMATICA
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Table[7^n/6 - 6^n/2 + 5^n/2 - 4^n/6, {n, 3, 20}] (* Vaclav Kotesovec, Nov 19 2012 *)
LinearRecurrence[{22, -179, 638, -840}, {1, 22, 305, 3410}, 20] (* Harvey P. Dale, Jan 09 2024 *)
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PROG
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(Magma) [7^n/6 - 6^n/2 + 5^n/2 - 4^n/6: n in [3..30]]; // Vincenzo Librandi, May 03 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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