A051306 Number of 6-element proper antichains of an n-element set.

0, 0, 0, 0, 0, 300, 233821, 78501094, 15532759830, 2213672795040, 254206334062527, 25146386270836578, 2235664320306737320, 183782806231396191820, 14248056393984957136593

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..550

Formula

a(n) = (1/6!)*(64^n -45*48^n +300*40^n -135*36^n +510*34^n -198*33^n -1499*32^n -2700*30^n +6615*28^n +1215*27^n -780*26^n +3750*25^n -6750*24^n -8280*23^n +3828*22^n -12285*21^n +19425*20^n +31635*19^n -30105*18^n -34425*17^n +24770*16^n +13125*15^n -3885*14^n +390*13^n -5670*12^n -12485*11^n +28575*10^n -16560*9^n -3435*8^n +7868*7^n -4995*6^n +3800*5^n -1301*4^n -822*3^n +668*2^n -120).

Mathematica

Table[(64^n - 45*48^n + 300*40^n - 135*36^n + 510*34^n - 198*33^n - 1499*32^n - 2700*30^n + 6615*28^n + 1215*27^n - 780*26^n + 3750*25^n - 6750*24^n - 8280*23^n + 3828*22^n - 12285*21^n + 19425*20^n + 31635*19^n - 30105*18^n - 34425*17^n + 24770*16^n + 13125*15^n - 3885*14^n + 390*13^n - 5670*12^n - 12485*11^n + 28575*10^n - 16560*9^n - 3435*8^n + 7868*7^n - 4995*6^n + 3800*5^n - 1301*4^n - 822*3^n + 668*2^n - 120)/6!, {n, 0, 50}] (* G. C. Greubel, Oct 07 2017 *)

Crossrefs

Cf. A032263, A036239, A051112.

Sequence in context: A063935 A294687 A015275 * A151609 A004225 A004226

Adjacent sequences: A051303 A051304 A051305 * A051307 A051308 A051309

Keyword

nonn

Author

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic

Status

approved