A340292 a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - sin(j*Pi/(2*n+1))^2 * sin(k*Pi/(2*n+1))^2).

1, 7, 4961, 371647151, 2952717950351617, 2489597262406609716450871, 222812636926792555435326125877303201, 2116840405025957772469476908228785308996001314527, 2134958300495920487325052422663717579194357002081033470045923329

Offset

0,2

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = A002315(n) * A340293(n)^2.

a(n) ~ exp(2*G*(2*n+1)^2/Pi) / 2^(4*n + 3/4), where G is Catalan's constant A006752. - Vaclav Kotesovec, Jan 04 2021

Mathematica

Table[2^(4*n^2) * Product[Product[1 - Sin[j*Pi/(2*n + 1)]^2 * Sin[k*Pi/(2*n + 1)]^2, {k, 1, n}], {j, 1, n}], {n, 0, 10}] // Round (* Vaclav Kotesovec, Jan 04 2021 *)

Prog

(PARI) default(realprecision, 120);
{a(n) = round(4^(2*n^2)*prod(j=1, n, prod(k=1, n, 1-(sin(j*Pi/(2*n+1))*sin(k*Pi/(2*n+1)))^2)))}

Crossrefs

Cf. A002315, A340166, A340291, A340293, A340295.

Sequence in context: A338250 A103856 A364640 * A095155 A219893 A243780

Adjacent sequences: A340289 A340290 A340291 * A340293 A340294 A340295

Keyword

nonn

Author

Seiichi Manyama, Jan 03 2021

Status

approved