A340165 a(n) = 4^((n-2)*(n-1)) * Product_{1<=i

1, 1, 19, 7056, 51251277, 7280323311888, 20225477546584790663, 1098876823994281426921193472, 1167619533875635661974056722756222809, 24263631353490502503207804571072304043237024000

Offset: 1

Author

Seiichi Manyama, Dec 30 2020

Keywords

• nonn

Crossrefs

Cf. A340139, A340167.

Programs

Mathematica

Table[4^((n-2)*(n-1)) * Product[Product[1 + Sin[i*Pi/(2*n)]^2 * Sin[j*Pi/(2*n)]^2, {i, 1, j-1}], {j, 2, n-1}], {n, 1, 12}] // Round (* Vaclav Kotesovec, Dec 31 2020 *)

PARI

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

Formula

a(n) = 4^((n-2)*(n-1)) * Product_{1<=i

a(n) ~ 2^(2*n^2 - 3*n + 35/8) * (1 - sqrt(2*sqrt(2)-2))^n * exp(2*A340350*n^2/Pi^2). - Vaclav Kotesovec, Jan 05 2021

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