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A340563 a(n) = sqrt( Product_{1<=j, k<=n-1} (4*sin(j*Pi/n)^2 + 4*cos(k*Pi/n)^2) ). 1
1, 1, 2, 16, 384, 30976, 7741440, 6369316864, 16435095011328, 138915523039657984, 3696387867279360000000, 321533678904455375050768384, 88192375153215003517412966400000, 78996127242669742603293261855977373696, 223311937686075869460797609709638544686841856 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * (sqrt(2) - 1)^n * exp(2*G*n^2/Pi), where c = sqrt(Pi) / Gamma(3/4)^2 if n is even and c = 2^(1/4) if n is odd, G is Catalan's constant A006752. - Vaclav Kotesovec, Mar 18 2023
MATHEMATICA
Table[Sqrt[Product[Product[(4*Sin[j*Pi/n]^2 + 4*Cos[k*Pi/n]^2), {j, 1, n - 1}], {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-1, prod(k=1, n-1, 4*sin(j*Pi/n)^2+4*cos(k*Pi/n)^2))))}
CROSSREFS
Main diagonal of A340561.
Sequence in context: A052737 A002474 A172149 * A295710 A012390 A009613
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 11 2021
STATUS
approved

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Last modified April 14 03:49 EDT 2024. Contains 371655 sequences. (Running on oeis4.)