A051307 Number of 7-element proper antichains of an n-element set.

0, 0, 0, 0, 0, 135, 329205, 365924948, 205640068950, 75013516525425, 20611869786684495, 4661763066154503606, 917701003163074793520, 163180081989646991509955, 26889766005753182579964345, 4182467653250525215771670424, 622388054953695081193665509610

Offset

0,6

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = 1/7! * (128^n -63*96^n +525*80^n -315*72^n +1785*68^n -1386*66^n +455*65^n -3486*64^n -9450*60^n +21315*56^n +8505*54^n -13650*52^n -5355*51^n +36750*50^n -5145*49^n -14805*48^n -57960*46^n -4725*45^n +45738*44^n +36120*43^n -191835*42^n +43050*41^n +74725*40^n -73710*39^n +333165*38^n +104895*37^n -73395*36^n -54390*35^n -354144*34^n -423192*33^n +383621*32^n +143220*31^n -292425*30^n +753855*29^n +181545*28^n -314685*27^n -114660*26^n -916125*25^n -268716*24^n +1998493*23^n +140833*22^n -2359350*21^n +458675*20^n +2147950*19^n -961758*18^n -1428000*17^n +933380*16^n +578175*15^n -614362*14^n +143052*13^n +45990*12^n -244860*11^n +356475*10^n -199521*9^n -12244*8^n +64778*7^n -40026*6^n +28035*5^n -9604*4^n -5292*3^n +4248*2^n -720).

Crossrefs

Cf. A032263, A036239, A051112.

Sequence in context: A273440 A106175 A203625 * A056740 A065663 A365328

Adjacent sequences: A051304 A051305 A051306 * A051308 A051309 A051310

Keyword

nonn

Author

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic

Status

approved