A059079 - OEIS

%I #7 Jun 14 2013 04:17:11

%S 2,5,19,16654,2369110564675,5960531437586238714806902334250676,

%T 479047836152505670895481840783987408043359908583921478726185296900312296071642855730299

%N Number of n-element T_0-antichains on a labeled set.

%C An antichain on a set is a T_0-antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point.

%D V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)

%D V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

%H Vladeta Jovovic, <a href="/A059079/a059079.pdf">Illustration</a>

%e a(0) = (1/0!)*[1!*e] = 2; a(1) = (1/1!)*[2!*e] = 5; a(2) = (1/2!)*([4!*e] - 2*[3!*e] + [2!*e]) = 19; a(3) = (1/3!)*([8!*e] - 6*[6!*e] + 6*[5!*e] + 3*[4!*e] - 6*[3!*e] + 2*[2!*e]) = 16654, where [n!*e]=floor(n!*exp(1)).

%Y Cf. A059080-A059083, A059048-A059052, A000522.

%K hard,nonn

%O 0,1

%A _Vladeta Jovovic_, Goran Kilibarda, Dec 23 2000