0,3

Excluding the empty set halves the entries.

a(n) is prime for n = 2, 3, 4. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 21 2005

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

M. Klazar, Extremal problems for ordered hypergraphs

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

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.rs), May 30 2004

Also exp(-x)*Sum(2^(2^n-1)*x^n/n!, n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 01 2004

(PARI) f(n)=sum(k=0, n, (-1)^k*n!/k!/(n-k)!*2^(2^(n-k)))/2;

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

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms and comments from Michael Somos