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%I #18 Sep 08 2022 08:45:01
%S 0,0,0,0,25,1895,70370,1868650,41062035,802349205,14514339340,
%T 249104207000,4120588431245,66392465654515,1049608974433110,
%U 16365222591176550,252584307401055655,3869412829938587825,58950765174112191680,894469325684769169300,13531152125348360663265
%N Number of 4-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 G. C. Greubel, <a href="/A056047/b056047.txt">Table of n, a(n) for n = 0..845</a>
%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) = (1/4!)*(15^n - 12*11^n + 24*9^n + 4*8^n - 18*7^n + 6*6^n - 36*5^n + 36*4^n + 11*3^n - 22*2^n + 6).
%F G.f.: -5*x^4*(517752*x^6 -251184*x^5 +4757*x^4 +12696*x^3 -1810*x^2 +24*x +5) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(11*x -1)*(15*x -1)). - _Colin Barker_, Jul 11 2013
%t Table[(1/4!)*(15^n - 12*11^n + 24*9^n + 4*8^n - 18*7^n + 6*6^n - 36*5^n + 36*4^n + 11*3^n - 22*2^n + 6), {n,0,25}] (* _G. C. Greubel_, Oct 07 2017 *)
%o (PARI) for(n=0,25, print1((15^n - 12*11^n + 24*9^n + 4*8^n - 18*7^n + 6*6^n - 36*5^n + 36*4^n + 11*3^n - 22*2^n + 6)/24, ", ")) \\ _G. C. Greubel_, Oct 07 2017
%o (Magma) [(15^n - 12*11^n + 24*9^n + 4*8^n - 18*7^n + 6*6^n - 36*5^n + 36*4^n + 11*3^n - 22*2^n + 6)/24: n in [0..25]]; // _G. C. Greubel_, Oct 07 2017
%Y Cf. A051112.
%K nonn,easy
%O 0,5
%A _Vladeta Jovovic_, Goran Kilibarda, Jul 25 2000
%E More terms from _Colin Barker_, Jul 11 2013
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