cp's OEIS Frontend

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.

A340181 a(n) = Product_{1<=j,k,m<=n} (4*sin(j*Pi/(2*n+1))^2 + 4*sin(k*Pi/(2*n+1))^2 + 4*sin(m*Pi/(2*n+1))^2).

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%I A340181 #20 Jan 05 2021 10:19:41
%S A340181 1,9,7486875,14334918272193811385583,
%T A340181 1483160703050490588200236172057973908184332257091136
%N A340181 a(n) = Product_{1<=j,k,m<=n} (4*sin(j*Pi/(2*n+1))^2 + 4*sin(k*Pi/(2*n+1))^2 + 4*sin(m*Pi/(2*n+1))^2).
%C A340181 (a(n)/((2n + 1)*3^n))^(1/3) is an integer.
%F A340181 Limit_{n->infinity} a(n)^(1/n^3) = exp(8*A340322/Pi^3). - _Vaclav Kotesovec_, Jan 05 2021
%t A340181 Round[Table[2^(n^3)* Product[3 - Cos[2*j*Pi/(2*n + 1)] - Cos[2*k*Pi/(2*n + 1)] - Cos[2*m*Pi/(2*n + 1)], {j, 1, n}, {k, 1, n}, {m, 1, n}], {n, 0, 5}]] (* _Vaclav Kotesovec_, Jan 04 2021 *)
%o A340181 (PARI) default(realprecision, 500);
%o A340181 {a(n) = round(prod(j=1, n, prod(k=1, n, prod(m=1, n, 4*sin(j*Pi/(2*n+1))^2+4*sin(k*Pi/(2*n+1))^2+4*sin(m*Pi/(2*n+1))^2))))}
%Y A340181 Cf. A124647, A127605, A340182, A340183.
%K A340181 nonn
%O A340181 0,2
%A A340181 _Seiichi Manyama_, Dec 31 2020