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Number of (k,m,n)-antichains of multisets with k=3 and m=6.
1

%I #15 Oct 08 2017 18:32:37

%S 0,0,0,15,1729366,10340309701,24380294253318,36539301527565851,

%T 42407896071362952494,42091311943805278602897,

%U 37781049596189171124466966,31727275407315883994852626087

%N Number of (k,m,n)-antichains of multisets with k=3 and m=6.

%C By a (k,m,n)-antichain of multisets we mean an m-antichain of k-bounded multisets on an n-set. A multiset is called k-bounded if every its element has the multiplicity not greater than k-1.

%H G. C. Greubel, <a href="/A084878/b084878.txt">Table of n, a(n) for n = 0..345</a>

%H Goran Kilibarda and Vladeta Jovovic, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Kilibarda/kili2.html">Antichains of Multisets</a>, J. Integer Seqs., Vol. 7, 2004.

%F a(n) = (1/6!)*(729^n - 30*486^n + 120*378^n + 60*324^n + 60*294^n - 360*279^n - 12*276^n - 720*252^n + 15*243^n + 90*234^n + 720*231^n + 120*216^n + 720*210^n - 240*205^n + 360*196^n - 720*189^n - 180*187^n + 720*186^n - 720*176^n + 120*168^n - 720*167^n + 360*165^n - 300*162^n - 720*157^n + 180*156^n + 720*148^n - 240*145^n + 720*138^n + 30*134^n - 240*129^n + 900*126^n - 360*120^n + 180*111^n + 300*108^n - 20*102^n + 150*98^n - 1800*93^n - 1800*84^n + 85*81^n + 450*78^n + 1800*77^n + 1800*70^n - 1800*63^n + 300*56^n - 1020*54^n + 2040*42^n + 340*36^n - 2040*31^n + 225*27^n + 510*26^n - 1350*18^n + 1350*14^n + 274*9^n - 548*6^n + 120*3^n).

%Y Cf. A016269, A047707, A051112-A051118, A084869-A084883.

%K nonn

%O 0,4

%A Goran Kilibarda, _Vladeta Jovovic_, Jun 10 2003