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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). 2
1, 9, 7486875, 14334918272193811385583, 1483160703050490588200236172057973908184332257091136 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
(a(n)/((2n + 1)*3^n))^(1/3) is an integer.
LINKS
FORMULA
Limit_{n->infinity} a(n)^(1/n^3) = exp(8*A340322/Pi^3). - Vaclav Kotesovec, Jan 05 2021
MATHEMATICA
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 *)
PROG
(PARI) default(realprecision, 500);
{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))))}
CROSSREFS
Sequence in context: A174001 A273234 A259159 * A131678 A229687 A029983
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 31 2020
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)