This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051303 #26 Sep 28 2024 14:45:14
%S A051303 0,0,0,1,30,605,9030,110901,1200150,11932285,111885510,1006471301,
%T A051303 8786447670,75039565965,630534185190,5234341175701,43059373189590,
%U A051303 351805681631645,2859550165976070,23152657123816101,186907026783617910,1505512392025329325
%N A051303 Number of 3-element proper antichains of an n-element set.
%H A051303 G. C. Greubel, <a href="/A051303/b051303.txt">Table of n, a(n) for n = 0..1000</a>
%H A051303 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (29,-343,2135,-7504,14756,-14832,5760).
%F A051303 a(n) = (8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!.
%F A051303 G.f.: x^3*(360*x^3-78*x^2-x-1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - _Colin Barker_, Nov 27 2012
%F A051303 a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7) for n > 6. - _Wesley Ivan Hurt_, Oct 06 2017
%F A051303 E.g.f.: exp(x)*(exp(x) - 1)^3*(2 - 2*exp(x) - 3*exp(2*x) + 3*exp(3*x) + exp(4*x))/6. - _Stefano Spezia_, Sep 28 2024
%p A051303 A051303:=n->(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!: seq(A051303(n), n=0..30); # _Wesley Ivan Hurt_, Oct 06 2017
%t A051303 Table[(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!, {n,0,25}] (* _G. C. Greubel_, Oct 06 2017 *)
%o A051303 (PARI) for(n=0,25, print1((8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2 )/3!, ", ")) \\ _G. C. Greubel_, Oct 06 2017
%o A051303 (Magma) [(8^n - 9*6^n + 15*5^n - 4*4^n - 9*3^n + 8*2^n - 2) / Factorial(3) : n in [0..25]]; // _G. C. Greubel_, Oct 06 2017
%Y A051303 Cf. A032263, A036239, A051112.
%K A051303 nonn,easy
%O A051303 0,5
%A A051303 _Vladeta Jovovic_, Goran Kilibarda, Zoran Maksimovic