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A084871 Number of 4-multiantichains of an n-set.

%I A084871 #17 Sep 08 2022 08:45:11
%S A084871 1,2,7,41,398,6177,128232,2881531,62769238,1288737197,25012685732,
%T A084871 463681018671,8294783320578,144410750517217,2462999084589232,
%U A084871 41359616334934211,686406989350511918,11290725888842193237
%N A084871 Number of 4-multiantichains of an n-set.
%H A084871 G. C. Greubel, <a href="/A084871/b084871.txt">Table of n, a(n) for n = 0..825</a>
%H A084871 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 A084871 a(n) = (16^n - 12*12^n + 24*10^n + 4*9^n - 6*8^n + 6*7^n - 108*6^n + 108*5^n + 83*4^n - 166*3^n + 90*2^n)/4!.
%F A084871 From _R. J. Mathar_, Jul 08 2011: (Start)
%F A084871 G.f.: (-1 + 80*x - 2813*x^2 + 57293*x^3 - 749139*x^4 + 6577949*x^5 - 39353597*x^6 + 158972472*x^7 - 417774220*x^8 + 651991536*x^9 - 465379200*x^10) / ( (9*x-1) *(6*x-1) *(7*x-1) *(3*x-1) *(5*x-1) *(2*x-1) *(12*x-1) *(10*x-1) *(4*x-1) *(8*x-1) *(16*x-1) ).
%F A084871 a(n) = 82*a(n-1) - 2970*a(n-2) + 62700*a(n-3) - 856713*a(n-4) + 7947786*a(n-5) - 51019100*a(n-6) + 226259000*a(n-7) - 678011136*a(n-8) + 1304341632*a(n-9) - 1445575680*a(n-10) + 696729600*a(n-11). (End)
%t A084871 Table[(16^n - 12*12^n + 24*10^n + 4*9^n - 6*8^n + 6*7^n - 108*6^n + 108*5^n + 83*4^n - 166*3^n + 90*2^n)/4!, {n, 0, 50}] (* _G. C. Greubel_, Oct 08 2017 *)
%o A084871 (PARI) for(n=0,50, print1((16^n - 12*12^n + 24*10^n + 4*9^n - 6*8^n + 6*7^n - 108*6^n + 108*5^n + 83*4^n - 166*3^n + 90*2^n)/4!, ", ")) \\ _G. C. Greubel_, Oct 08 2017
%o A084871 (Magma) [(16^n - 12*12^n + 24*10^n + 4*9^n - 6*8^n + 6*7^n - 108*6^n + 108*5^n + 83*4^n - 166*3^n + 90*2^n)/24: n in [0..50]]; // _G. C. Greubel_, Oct 08 2017
%Y A084871 Cf. A016269, A047707, A051112-A051118, A084869-A084883.
%K A084871 nonn
%O A084871 0,2
%A A084871 Goran Kilibarda, _Vladeta Jovovic_, Jun 10 2003