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A059082 Number of 6-element T_0-antichains on a labeled n-set, n = 0, ..., 64.

%I A059082 #15 Sep 04 2017 18:05:06
%S A059082 0,0,0,0,1,1370,738842,176796382,26021566536,2807549333568,
%T A059082 245222809302240,18418417704308160,1236761946163054080,
%U A059082 76210520306627266560,4388527139331858082560,239214759548062858560000,12457699161320493400320000,623967599346727576292352000
%N A059082 Number of 6-element T_0-antichains on a labeled n-set, n = 0, ..., 64.
%C A059082 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 A059082 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 A059082 V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H A059082 Alois P. Heinz, <a href="/A059082/b059082.txt">Table of n, a(n) for n = 0..64</a>
%H A059082 V. Jovovic, <a href="/A059083/a059083.pdf">Formula for the number of m-element T_0-antichains on a labeled n-set</a>
%F A059082 a(n) = (1/6!)*([64]_n - 30*[48]_n + 120*[40]_n + 60*[36]_n + 60*[34]_n - 12*[33]_n - 345*[32]_n - 720*[30]_n + 810*[28]_n + 120*[27]_n + 480*[26]_n + 360*[25]_n - 480*[24]_n - 720*[23]_n - 240*[22]_n - 540*[21]_n + 1380*[20]_n + 750*[19]_n + 60*[18]_n - 210*[17]_n - 1535*[16]_n - 1820*[15]_n + 2250*[14]_n + 1800*[13]_n - 2820*[12]_n + 300*[11]_n + 2040*[10]_n + 340*[9]_n - 1815*[8]_n + 510*[7]_n - 1350*[6]_n + 1350*[5]_n + 274*[4]_n - 548*[3]_n + 120*[2]_n), where [k]_n := k*(k - 1)*...*(k - n + 1), [k]_0 = 1.
%p A059082 f:=proc(k,n) if k+1<=n then RETURN(0) else RETURN(k!/(k - n)!) fi: end;a:=n->(1/6!)*(f(64,n) - 30*f(48,n) + 120*f(40,n) + 60*f(36,n) + 60*f(34,n)- 12*f(33,n) - 345*f(32,n) - 720*f(30,n) + 810*f(28,n) + 120*f(27,n) + 480*f(26,n) + 360*f(25,n) - 480*f(24,n) - 720*f(23,n) - 240*f(22,n) - 540*f(21,n) + 1380*f(20,n) + 750*f(19,n) + 60*f(18,n) - 210*f(17,n) - 1535*f(16,n) - 1820*f(15,n) + 2250*f(14,n) + 1800*f(13,n) - 2820*f(12,n) + 300*f(11,n) + 2040*f(10,n) + 340*f(9,n) - 1815*f(8,n) + 510*f(7,n) - 1350*f(6,n) + 1350*f(5,n) + 274*f(4,n) - 548*f(3,n) + 120*f(2,n));seq(a(n),n=0..20); # Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005
%Y A059082 Cf. A059079, A059080, A059081, A059083, A059048, A059049, A059050, A059051, A059052.
%K A059082 nonn,easy,fini,full
%O A059082 0,6
%A A059082 _Vladeta Jovovic_, Goran Kilibarda, Jan 06 2001
%E A059082 More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005