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A059081 Number of 5-element T_0-antichains on a labeled n-set, n=0,..,32. 3
0, 0, 0, 0, 6, 2086, 273072, 19371912, 940055760, 35289051840, 1099827892800, 29723466326400, 716351882400000, 15683016533184000, 315722887044364800, 5890186860509952000, 102288867798813696000, 1656523525703574528000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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.

REFERENCES

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)

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..32

Vladeta Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set

FORMULA

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A059079, A059080, A059082, A059083, A059048-A059052.

Sequence in context: A279440 A004817 A089535 * A226461 A172943 A182789

Adjacent sequences:  A059078 A059079 A059080 * A059082 A059083 A059084

KEYWORD

nonn,fini,full

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

STATUS

approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)