%I #13 Oct 08 2017 14:13:12
%S 0,0,0,0,112,39761,5318420,506289623,41378309308,3133123494417,
%T 227657567966500,16152548751321851,1129224692910819164,
%U 78169242144478858373,5373159786842137703140,367368738925063893430959
%N Number of 6-element families of an n-element set such that every 4 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="/A051366/b051366.txt">Table of n, a(n) for n = 0..550</a>
%F a(n) = (1/6!)*(64^n - 15*60^n + 60*58^n + 25*57^n - 240*56^n + 45*55^n + 705*54^n - 987*53^n - 351*52^n + 3040*51^n - 5445*50^n + 6105*49^n - 4939*48^n + 2997*47^n - 1365*46^n + 455*45^n - 105*44^n + 15*43^n - 42^n - 15*32^n + 75*30^n - 150*29^n + 150*28^n - 75*27^n + 15*26^n + 85*16^n - 85*15^n - 225*8^n + 225*7^n + 274*4^n - 274*3^n - 120*2^n + 120).
%t Table[1/6! (64^n - 15*60^n + 60*58^n + 25*57^n - 240*56^n + 45*55^n + 705*54^n - 987*53^n - 351*52^n + 3040*51^n - 5445*50^n + 6105*49^n - 4939*48^n + 2997*47^n - 1365*46^n + 455*45^n - 105*44^n + 15*43^n - 42^n - 15*32^n + 75*30^n - 150*29^n + 150*28^n - 75*27^n + 15*26^n + 85*16^n - 85*15^n - 225*8^n + 225*7^n + 274*4^n - 274*3^n - 120*2^n + 120), {n, 0, 50}] (* _G. C. Greubel_, Oct 08 2017 *)
%Y Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.
%K nonn
%O 0,5
%A _Vladeta Jovovic_, Goran Kilibarda