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 A328735 #18 Mar 20 2023 05:00:46
%S A328735 1,0,14,72,882,8400,95180,1060080,12389650,146472480,1767391164,
%T A328735 21581516880,266718438756,3327025429728,41849031952728,
%U A328735 530135326392672,6757845419895570,86619827323917888,1115719258312182524,14434274832755201424,187477238295444829732
%N A328735 Constant term in the expansion of (x + y + z + 1/x + 1/y + 1/z + x*y + y*z + z*x + 1/(x*y) + 1/(y*z) + 1/(z*x) + x*y*z + 1/(x*y*z))^n.
%F A328735 a(n) = Sum_{i=0..n} (-2)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^4.
%F A328735 From _Vaclav Kotesovec_, Mar 20 2023: (Start)
%F A328735 Recurrence: n^3*a(n) = 2*(n-1)*n*(2*n - 1)*a(n-1) + 112*(n-1)^3*a(n-2) + 184*(n-2)*(n-1)*(2*n - 3)*a(n-3) + 336*(n-3)*(n-2)*(n-1)*a(n-4).
%F A328735 a(n) ~ 2^(n-4) * 7^(n + 3/2) / (Pi^(3/2) * n^(3/2)). (End)
%t A328735 Table[Sum[(-2)^(n-i)*Binomial[n,i] * Sum[Binomial[i,j]^4, {j,0,i}], {i,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 20 2023 *)
%o A328735 (PARI) {a(n) = polcoef(polcoef(polcoef((-2+(1+x)*(1+y)*(1+z)+(1+1/x)*(1+1/y)*(1+1/z))^n, 0), 0), 0)}
%o A328735 (PARI) {a(n) = sum(i=0, n, (-2)^(n-i)*binomial(n, i)*sum(j=0, i, binomial(i, j)^4))}
%Y A328735 Column k=4 of A328748.
%Y A328735 Sum_{i=0..n} (-2)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^m: A126869 (m=2), A002898 (m=3), this sequence (m=4), A328751 (m=5).
%Y A328735 Cf. A002899, A005260, A328725.
%K A328735 nonn
%O A328735 0,3
%A A328735 _Seiichi Manyama_, Oct 26 2019