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%I #10 Sep 08 2022 08:44:59
%S 0,0,0,0,5,780,41545,1442910,39400305,923889960,19550316665,
%T 384954289170,7196416532305,129495073447740,2264887575116985,
%U 38775513868485030,653195404307491505,10869004241198535120,179171681947204584505,2932562923651659410490,47737465871974206925905
%N Number of 4-element proper antichains of an n-element set.
%H G. C. Greubel, <a href="/A051304/b051304.txt">Table of n, a(n) for n = 0..825</a>
%F a(n) = (1/4!) * (16^n -18*12^n +60*10^n -9*9^n -102*8^n +105*7^n -90*6^n +95*5^n -31*4^n -33*3^n +28*2^n -6).
%F G.f. x^4*( 5 +365*x -7935*x^2 +46885*x^3 -191420*x^4 +2285460*x^5 -14380560*x^6 +27216000*x^7 ) / ( (x-1) *(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) ). - _R. J. Mathar_, Jun 13 2013
%t Table[(16^n - 18*12^n + 60*10^n - 9*9^n - 102*8^n + 105*7^n - 90*6^n + 95*5^n - 31*4^n - 33*3^n + 28*2^n - 6)/4!, {n, 0, 50}] (* _G. C. Greubel_, Oct 07 2017 *)
%o (PARI) for(n=0,50, print1((16^n - 18*12^n + 60*10^n - 9*9^n - 102*8^n + 105*7^n - 90*6^n + 95*5^n - 31*4^n - 33*3^n + 28*2^n - 6)/4!, ", ")) \\ _G. C. Greubel_, Oct 07 2017
%o (Magma) [(16^n - 18*12^n + 60*10^n - 9*9^n - 102*8^n + 105*7^n - 90*6^n + 95*5^n - 31*4^n - 33*3^n + 28*2^n - 6)/(24): n in [0..50]]; // _G. C. Greubel_, Oct 07 2017
%Y Cf. A032263, A036239, A051112.
%K nonn
%O 0,5
%A _Vladeta Jovovic_, Goran Kilibarda, Zoran Maksimovic
%E Terms a(16) onward added by _G. C. Greubel_, Oct 07 2017
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