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 A361704 #10 Mar 25 2023 07:48:25
%S A361704 1,1,1,1,1,1,361,2521,10081,30241,75601,166321,1580041,16833961,
%T A361704 114594481,569368801,2273150881,7723366561,30024671041,193227592321,
%U A361704 1460787267601,9492136169041,50996729017081,232560967743721,973251617544361,4464217099881001
%N A361704 Constant term in the expansion of (1 + w^2 + x^2 + y^2 + z^2 + 1/(w*x*y*z))^n.
%F A361704 a(n) = Sum_{k=0..floor(n/6)} (4*k)!/k!^4 * binomial(6*k,4*k) * binomial(n,6*k).
%F A361704 From _Vaclav Kotesovec_, Mar 25 2023: (Start)
%F A361704 Recurrence: (n-3)*n^4*a(n) = (6*n^5 - 30*n^4 + 50*n^3 - 45*n^2 + 21*n - 4)*a(n-1) - (n-1)*(15*n^4 - 90*n^3 + 195*n^2 - 195*n + 76)*a(n-2) + 5*(n-2)*(n-1)*(4*n^3 - 24*n^2 + 48*n - 33)*a(n-3) - 5*(n-3)*(n-2)*(n-1)*(3*n^2 - 15*n + 19)*a(n-4) + 6*(n-4)*(n-3)^2*(n-2)*(n-1)*a(n-5) + 11663*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6).
%F A361704 a(n) ~ sqrt(7 + 9/(4*2^(1/3)) + 433/(48*2^(2/3))) * (1 + 3*2^(2/3))^n / (Pi^2 * n^2). (End)
%t A361704 Table[Sum[(4*k)!/k!^4 * Binomial[6*k,4*k] * Binomial[n,6*k], {k,0,n/6}], {n,0,25}] (* _Vaclav Kotesovec_, Mar 25 2023 *)
%o A361704 (PARI) a(n) = sum(k=0, n\6, (4*k)!/k!^4*binomial(6*k, 4*k)*binomial(n, 6*k));
%Y A361704 Cf. A361675, A361703, A361705.
%K A361704 nonn,easy
%O A361704 0,7
%A A361704 _Seiichi Manyama_, Mar 21 2023