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%I #14 Oct 07 2017 15:13:31
%S 0,0,0,0,6,2086,273072,19371912,940055760,35289051840,1099827892800,
%T 29723466326400,716351882400000,15683016533184000,315722887044364800,
%U 5890186860509952000,102288867798813696000,1656523525703574528000
%N Number of 5-element T_0-antichains on a labeled n-set, n=0,..,32.
%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 G. C. Greubel, <a href="/A059081/b059081.txt">Table of n, a(n) for n = 0..32</a>
%H Vladeta Jovovic, <a href="/A059083/a059083.pdf">Formula for the number of m-element T_0-antichains on a labeled n-set</a>
%F a(n) = (1/5!)*([32]_n - 20*[24]_n + 60*[20]_n + 20*[18]_n + 10*[17]_n - 110*[16]_n - 120*[15]_n + 150*[14]_n + 120*[13]_n - 240*[12]_n + 20*[11]_n + 240*[10]_n + 40*[9]_n - 205*[8]_n + 60*[7]_n - 210*[6]_n + 210*[5]_n + 50*[4]_n - 100*[3]_n + 24*[2]_n), where [k]_n := k*(k - 1)*...*(k - n + 1), [k]_0 = 1.
%t P[x_, n_] := (-1)^n*Pochhammer[-x, n]; Table[(1/5!)*(P[32, n] - 20*P[24, n] + 60*P[20, n] + 20*P[18, n] + 10*P[17, n] - 110*P[16, n] - 120*P[15, n] + 150*P[14, n] + 120*P[13, n] - 240*P[12, n] + 20*P[11, n] + 240*P[10, n] + 40*P[9, n] - 205*P[8, n] + 60*P[7, n] - 210*P[6, n] + 210*P[5, n] + 50*P[4, n] - 100*P[3, n] + 24*P[2, n]), {n, 0, 32}] (* _G. C. Greubel_, Oct 07 2017 *)
%Y Cf. A059079, A059080, A059082, A059083, A059048-A059052.
%K nonn,fini,full
%O 0,5
%A _Vladeta Jovovic_, Goran Kilibarda, Jan 06 2001
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