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Number of 7-antichain covers of a labeled n-set.
6

%I #9 Jun 17 2013 03:20:25

%S 490,1305330,1076513148,474700998300,143480504528862,

%T 33962870686689270,6808412143396065136,1214116433267798496480,

%U 198951942958529631990834,30633642863234275154265690,4502737302793395778228384164

%N Number of 7-antichain covers of a labeled n-set.

%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 K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cover.html">Antichain covers</a>

%F a(n)=(1/7!)*(127^n - 42*95^n + 210*79^n + 140*71^n + 210*67^n - 84*65^n + 14*64^n - 819*63^n - 2520*59^n + 2730*55^n + 840*53^n + 840*51^n - 420*50^n + 2940*49^n + 630*47^n - 5040*45^n + 840*44^n - 1260*43^n + 1680*42^n - 9660*41^n + 1260*40^n + 3360*39^n - 7560*38^n + 11130*37^n + 5880*36^n + 9240*35^n + 2982*34^n - 6300*33^n - 8652*32^n - 9905*31^n - 8400*30^n - 8540*29^n + 13860*28^n + 14490*27^n - 5040*26^n + 10500*25^n + 10080*24^n - 8120*23^n - 15050*22^n - 5040*21^n - 11340*20^n + 20580*19^n + 15750*18^n - 1540*17^n - 5810*16^n - 16485*15^n - 21420*14^n + 26250*13^n + 21000*12^n - 29820*11^n + 3500*10^n + 17640*9^n + 2940*8^n - 16016*7^n + 4410*6^n - 9744*5^n + 9744*4^n + 1764*3^n - 3528*2^n + 720).

%Y Cf. A051115.

%K nonn

%O 5,1

%A _Vladeta Jovovic_, Goran Kilibarda, Zoran Maksimovic, Jul 25 2000