A340293 a(n) = 4^((n-1)*n) * Product_{1<=j

1, 1, 11, 1247, 1455913, 17511093953, 2169916151129091, 2770393222231417622719, 36443188794328204864735075793, 4939371777650229260975457785579794433, 6897784079863728378183626237683602071537213179

Offset: 0

Author

Seiichi Manyama, Jan 03 2021

Keywords

• nonn

Crossrefs

Cf. A340185, A340292.

Programs

Mathematica

Table[2^(2*n*(n-1)) * Product[Product[1 - Sin[j*Pi/(2*n + 1)]^2*Sin[k*Pi/(2*n + 1)]^2, {k, j+1, n}], {j, 1, n}], {n, 0, 12}] // Round (* Vaclav Kotesovec, Jan 04 2021 *)

PARI

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

Formula

a(n) ~ exp(G*(2*n+1)^2/Pi) / (2^(2*n - 1/8) * (1 + sqrt(2))^(n + 1/2)), where G is Catalan's constant A006752. - Vaclav Kotesovec, Jan 04 2021