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A084872 Number of 5-multiantichains of an n-set.

%I A084872 #16 Sep 08 2022 08:45:11
%S A084872 1,2,8,56,726,17938,722680,35955180,1798971434,83885891894,
%T A084872 3612380896332,145277787750064,5534505187364062,202229611397865690,
%U A084872 7158136006402746464,247316732670273773108,8389241054998193347410
%N A084872 Number of 5-multiantichains of an n-set.
%H A084872 G. C. Greubel, <a href="/A084872/b084872.txt">Table of n, a(n) for n = 0..660</a>
%H A084872 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 A084872 a(n) = (1/5!)*(32^n - 20*24^n + 60*20^n + 20*18^n + 10*17^n - 90*16^n - 120*15^n + 150*14^n + 120*13^n - 480*12^n + 20*11^n + 720*10^n + 120*9^n - 445*8^n + 180*7^n - 1650*6^n + 1650*5^n + 870*4^n - 1740*3^n + 744*2^n).
%t A084872 Table[(32^n - 20*24^n + 60*20^n + 20*18^n + 10*17^n - 90*16^n - 120*15^n + 150*14^n + 120*13^n - 480*12^n + 20*11^n + 720*10^n + 120*9^n - 445*8^n + 180*7^n - 1650*6^n + 1650*5^n + 870*4^n - 1740*3^n + 744*2^n)/120, {n, 0, 50}] (* _G. C. Greubel_, Oct 08 2017 *)
%o A084872 (PARI) for(n=0,50, print1((32^n - 20*24^n + 60*20^n + 20*18^n + 10*17^n - 90*16^n - 120*15^n + 150*14^n + 120*13^n - 480*12^n + 20*11^n + 720*10^n + 120*9^n - 445*8^n + 180*7^n - 1650*6^n + 1650*5^n + 870*4^n - 1740*3^n + 744*2^n)/120, ", ")) \\ _G. C. Greubel_, Oct 08 2017
%o A084872 (Magma) [(32^n - 20*24^n + 60*20^n + 20*18^n + 10*17^n - 90*16^n - 120*15^n + 150*14^n + 120*13^n - 480*12^n + 20*11^n + 720*10^n + 120*9^n - 445*8^n + 180*7^n - 1650*6^n + 1650*5^n + 870*4^n - 1740*3^n + 744*2^n)/120: n in [0..50]]; // _G. C. Greubel_, Oct 08 2017
%Y A084872 Cf. A016269, A047707, A051112-A051118, A084869-A084883.
%K A084872 nonn
%O A084872 0,2
%A A084872 Goran Kilibarda, _Vladeta Jovovic_, Jun 10 2003