A340139 a(n) = 4^((n-2)*(n-1)) * Product_{1<=i

1, 1, 13, 1904, 3016365, 50771120400, 8993476465721657, 16670531837245286776832, 322175275214070402711647486361, 64754609334534873770923002355900227840

Offset: 1

Author

Seiichi Manyama, Dec 29 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..45

Crossrefs

Cf. A007725.

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) ~ sqrt(Gamma(1/4)) * exp(4*G*n^2/Pi) / (Pi^(3/8) * n^(3/4) * 2^(3*n - 9/4) * (1 + sqrt(2))^n), where G is Catalan's constant A006752. - Vaclav Kotesovec, Jan 05 2021

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