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A336182 a(n) = Sum_{k=0..n} (-3)^k * binomial(n,k)^3.

%I A336182 #22 Jul 13 2020 03:43:28
%S A336182 1,-2,-14,136,106,-8492,35344,395008,-4547462,-4838372,365951356,
%T A336182 -1601617712,-19715085584,233866581856,285409397056,-20406741254144,
%U A336182 90043530872218,1169513126877676,-13961261999882204,-18779832792734384,1270510266589738636,-5584024444211882792
%N A336182 a(n) = Sum_{k=0..n} (-3)^k * binomial(n,k)^3.
%C A336182 Diagonal of the rational function 1 / (1 + y + z + x*y + y*z - 3*z*x - 2*x*y*z).
%C A336182 Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) + 3*x*y*z).
%H A336182 Robert Israel, <a href="/A336182/b336182.txt">Table of n, a(n) for n = 0..1020</a>
%F A336182 From _Robert Israel_, Jul 12 2020: (Start)
%F A336182 a(n) = hypergeom([-n,-n,-n],[1,1],3).
%F A336182 (24*n^3 + 176*n^2 + 416*n + 320)*a(n + 1) + (279*n^3 + 2325*n^2 + 6382*n + 5776)*a(n + 2) + (18*n^3 + 168*n^2 + 514*n + 512)*a(n + 3) + (3*n^3 + 31*n^2 + 104*n + 112)*a(n + 4)=0. (End)
%p A336182 f:= gfun:-rectoproc({(24*n^3 + 176*n^2 + 416*n + 320)*a(n + 1) + (279*n^3 + 2325*n^2 + 6382*n + 5776)*a(n + 2) + (18*n^3 + 168*n^2 + 514*n + 512)*a(n + 3) + (3*n^3 + 31*n^2 + 104*n + 112)*a(n + 4), a(0) = 1, a(1) = -2, a(2) = -14, a(3) = 136},a(n),remember):
%p A336182 map(f, [$0..30]); # _Robert Israel_, Jul 12 2020
%t A336182 a[n_] := Sum[(-3)^k * Binomial[n, k]^3, {k, 0, n}]; Array[a, 22, 0] (* _Amiram Eldar_, Jul 11 2020 *)
%o A336182 (PARI) {a(n) = sum(k=0, n, (-3)^k*binomial(n,k)^3)}
%Y A336182 Column k=3 of A336179.
%Y A336182 Cf. A206180.
%K A336182 sign
%O A336182 0,2
%A A336182 _Seiichi Manyama_, Jul 10 2020