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%I #15 Oct 08 2017 18:09:34
%S 0,0,0,114,649850,678772108,377819587984,153135104560046,
%T 51758494975477206,15644366957608679376,4400899140179858419388,
%U 1180668574169021790713938,306827161657039584492179842
%N Number of (k,m,n)-antichains of multisets with k=3 and m=5.
%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="/A084877/b084877.txt">Table of n, a(n) for n = 0..415</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) = (1/5!)*(243^n - 20*162^n + 60*126^n + 20*108^n + 10*98^n - 120*93^n - 120*84^n + 10*81^n + 30*78^n + 120*77^n + 120*70^n - 120*63^n + 20*56^n - 120*54^n + 240*42^n + 40*36^n - 240*31^n + 35*27^n + 60*26^n - 210*18^n + 210*14^n + 50*9^n - 100*6^n + 24*3^n).
%t Table[(1/5!)*(243^n - 20*162^n + 60*126^n + 20*108^n + 10*98^n - 120*93^n - 120*84^n + 10*81^n + 30*78^n + 120*77^n + 120*70^n - 120*63^n + 20*56^n - 120*54^n + 240*42^n + 40*36^n - 240*31^n + 35*27^n + 60*26^n - 210*18^n + 210*14^n + 50*9^n - 100*6^n + 24*3^n), {n, 0, 1000}] (* _G. C. Greubel_, Oct 08 2017 *)
%Y Cf. A016269, A047707, A051112-A051118, A084869-A084883.
%K nonn
%O 0,4
%A Goran Kilibarda, _Vladeta Jovovic_, Jun 10 2003
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