A341479 - OEIS

A341479

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

1, 8, 256, 80000, 268435456, 9503683872768, 3503536769037500416, 13371518717864846127300608, 527073330112110826119518513790976, 214344906329057967318939007805581230080000

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..9.

FORMULA

a(n) ~ 2 * exp(4*G*n^2/Pi), where G is Catalan's constant A006752. - Vaclav Kotesovec, Feb 14 2021

MATHEMATICA

Table[Product[4*Sin[(2*j - 1)*Pi/(2*n)]^2 + 4*Sin[(2*k - 1)*Pi/(2*n)]^2, {k, 1, n}, {j, 1, n}], {n, 0, 12}] // Round (* Vaclav Kotesovec, Feb 14 2021 *)

PROG

(PARI) default(realprecision, 120);

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

CROSSREFS

Cf. A335586, A340562, A341478, A341493.

Sequence in context: A140338 A140339 A103488 * A041487 A034988 A230271

Adjacent sequences: A341476 A341477 A341478 * A341480 A341481 A341482

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 13 2021

STATUS

approved