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Search: id:A003465
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| A003465 |
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Number of ways to cover an n-set.
(Formerly M4024)
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+0
9
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| 1, 1, 5, 109, 32297, 2147321017, 9223372023970362989, 170141183460469231667123699502996689125, 57896044618658097711785492504343953925273862865136528166133547991141168899281
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Excluding the empty set halves the entries.
a(n) is prime for n = 2, 3, 4. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Jul 21 2005
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 165.
T. Hearne and C. G. Wagner, Minimal covers of finite sets, Discr. Math. 5 (1973), 247-251.
A. J. Macula, Covers of a finite set, Math. Mag., 67 (1994), 141-144.
C. G. Wagner, Covers of finite sets, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 515-520.
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LINKS
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M. Klazar, Extremal problems for ordered hypergraphs
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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sum((-1)^k*binomial(n, k)2^2^(n-k), k=0..n)/2.
E.g.f.: (1/2)*Sum(exp((2^n-1)*x)*ln(2)^n/n!, n=0..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 30 2004
Also exp(-x)*Sum(2^(2^n-1)*x^n/n!, n=0..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jun 01 2004
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PROGRAM
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(PARI) f(n)=sum(k=0, n, (-1)^k*n!/k!/(n-k)!*2^(2^(n-k)))/2;
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CROSSREFS
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Cf. A007537.
Cf. A055154 (row sums).
Sequence in context: A014180 A012122 A012091 this_sequence A053133 A002400 A086805
Adjacent sequences: A003462 A003463 A003464 this_sequence A003466 A003467 A003468
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms and comments from Michael Somos
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