%I #12 Dec 17 2022 12:43:13
%S 1,3,64,8022,6822072,14068794534,26314469636622,37310026340520678,
%T 42667193588371160460,42169580808988409450310,
%U 37803058273249518925923210,31733179110752959606870643334
%N Number of (k,m,n)-multiantichains of multisets with k=3 and m=6.
%C By a (k,m,n)-multiantichain of multisets we mean an m-multiantichain of k-bounded multisets on an n-set. The elements of a multiantichain could have the multiplicities greater than 1. A multiset is called k-bounded if every its element has the multiplicity not greater than k-1.
%H Goran Kilibarda and Vladeta Jovovic, <a href="https://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 + 45*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 - 900*162^n - 720*157^n + 180*156^n + 720*148^n - 240*145^n + 720*138^n + 30*134^n - 240*129^n + 2700*126^n - 360*120^n + 180*111^n + 900*108^n - 20*102^n + 450*98^n - 5400*93^n - 5400*84^n + 685*81^n + 1350*78^n + 5400*77^n + 5400*70^n - 5400*63^n + 900*56^n - 8220*54^n + 16440*42^n + 2740*36^n - 16440*31^n + 4275*27^n + 4110*26^n - 25650*18^n + 25650*14^n + 10474*9^n - 20948*6^n + 7560*3^n).
%Y Cf. A016269, A047707, A051112-A051118, A084869-A084882.
%K nonn
%O 0,2
%A Goran Kilibarda, _Vladeta Jovovic_, Jun 10 2003