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%I #17 Sep 08 2022 08:44:59
%S 0,0,0,3,275,8475,192385,3831093,71466675,1285857975,22632300245,
%T 392522268633,6734698919575,114576024346875,1935649374363705,
%U 32505459713369373,543014736097852475,9029329231317194175,149522990698790644765,2466942184607949641313
%N Number of 4-element families of an n-element set such that every 3 members of the family have a nonempty intersection.
%D V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).
%H G. C. Greubel, <a href="/A051365/b051365.txt">Table of n, a(n) for n = 0..825</a>
%F a(n) = (1/4!)*(16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6).
%F G.f.: -x^3*(47062848*x^7 -42816008*x^6 +13976678*x^5 -2170583*x^4 +168932*x^3 -5672*x^2 +2*x +3) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(7*x -1)*(8*x -1)*(11*x -1)*(12*x -1)*(13*x -1)*(14*x -1)*(16*x -1)). - _Colin Barker_, Jul 12 2013
%t Table[1/4! (16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6), {n, 0, 50}] (* _G. C. Greubel_, Oct 08 2017 *)
%o (PARI) for(n=0,50, print1((16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6)/24, ", ")) \\ _G. C. Greubel_, Oct 08 2017
%o (Magma) [(16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6)/24: n in [0..50]]; // _G. C. Greubel_, Oct 08 2017
%Y Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.
%K nonn,easy
%O 0,4
%A _Vladeta Jovovic_, Goran Kilibarda
%E More terms from _Colin Barker_, Jul 12 2013
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