A051305 Number of 5-element proper antichains of an n-element set.

0, 0, 0, 0, 0, 543, 118629, 12564636, 907001550, 51751693161, 2527016053023, 110737868741742, 4489929936371880, 171944175793168779, 6309813148166785257, 224210698542088771968

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..660

Formula

a(n) = (1/5!)*(32^n -30*24^n +150*20^n -45*18^n +85*17^n -515*16^n -450*15^n +1365*14^n +390*13^n -1680*12^n -22*11^n +1875*10^n -1080*9^n -685*8^n +980*7^n -669*6^n +575*5^n -195*4^n -150*3^n +124*2^n -24).

Mathematica

Table[(32^n - 30*24^n + 150*20^n - 45*18^n + 85*17^n - 515*16^n -450*15^n + 1365*14^n + 390*13^n - 1680*12^n - 22*11^n + 1875*10^n - 1080*9^n - 685*8^n + 980*7^n - 669*6^n + 575*5^n - 195*4^n - 150*3^n + 124*2^n - 24)/5!, {n, 0, 50}] (* G. C. Greubel, Oct 07 2017 *)

Prog

(PARI) for(n=0, 50, print1((32^n - 30*24^n + 150*20^n - 45*18^n + 85*17^n - 515*16^n -450*15^n + 1365*14^n + 390*13^n - 1680*12^n - 22*11^n + 1875*10^n - 1080*9^n - 685*8^n + 980*7^n - 669*6^n + 575*5^n - 195*4^n - 150*3^n + 124*2^n - 24)/5!, ", ")) \\ G. C. Greubel, Oct 07 2017
(Magma) [(32^n - 30*24^n + 150*20^n - 45*18^n + 85*17^n - 515*16^n -450*15^n + 1365*14^n + 390*13^n - 1680*12^n - 22*11^n + 1875*10^n - 1080*9^n - 685*8^n + 980*7^n - 669*6^n + 575*5^n - 195*4^n - 150*3^n + 124*2^n - 24)/(120): n in [0..50]]; // G. C. Greubel, Oct 07 2017

Crossrefs

Cf. A032263, A036239, A051112.

Sequence in context: A074888 A250854 A250685 * A204732 A204725 A266136

Adjacent sequences: A051302 A051303 A051304 * A051306 A051307 A051308

Keyword

nonn

Author

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic

Status

approved