|
|
A341782
|
|
a(n) = sqrt( Product_{j=1..n} Product_{k=1..n-1} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin(2*k*Pi/n)^2) ).
|
|
3
|
|
|
1, 1, 2, 112, 2312, 1270016, 292820000, 1522266730496, 3772667519238272, 193509323594243571712, 5041011532336819845120512, 2610531939025273190037188509696
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ exp(2*G*n^2/Pi) / (2^(3/4) * (1 + (1 + (-1)^n)/sqrt(2))), where G is Catalan's constant A006752. - Vaclav Kotesovec, Mar 18 2023
|
|
MATHEMATICA
|
Table[Sqrt[Product[Product[(4*Sin[(2*j - 1)*Pi/(2*n)]^2 + 4*Sin[2*k*Pi/n]^2), {j, 1, n}], {k, 1, n - 1}]], {n, 0, 15}] // Round (* Vaclav Kotesovec, Mar 18 2023 *)
|
|
PROG
|
(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, n-1, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin(2*k*Pi/n)^2))));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|