A340563 a(n) = sqrt( Product_{1<=j, k<=n-1} (4*sin(j*Pi/n)^2 + 4*cos(k*Pi/n)^2) ).

1, 1, 2, 16, 384, 30976, 7741440, 6369316864, 16435095011328, 138915523039657984, 3696387867279360000000, 321533678904455375050768384, 88192375153215003517412966400000, 78996127242669742603293261855977373696, 223311937686075869460797609709638544686841856

Offset

0,3

Links

Table of n, a(n) for n=0..14.

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.

Cf. A127606, A340562.

Sequence in context: A002474 A375059 A172149 * A295710 A012390 A009613

Adjacent sequences: A340560 A340561 A340562 * A340564 A340565 A340566

Keyword

nonn

Author

Seiichi Manyama, Jan 11 2021

Status

approved