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A340291 a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - cos(j*Pi/(2*n+1))^2 * cos(k*Pi/(2*n+1))^2). 4
1, 15, 32625, 8238791743, 230629380093001665, 703130165949449759361247759, 231459008314298532714943209968328640625, 8186710889725936196671113787217620194601044287109375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..7.

FORMULA

a(n) = A093967(2*n+1) * A340185(n)^2.

a(n) ~ Gamma(1/4) * exp(2*G*(2*n+1)^2/Pi) / (Pi^(3/4) * sqrt(n) * 2^(2*n + 2)), where G is the Catalan's constant A006752. - Vaclav Kotesovec, Jan 03 2021

MATHEMATICA

Table[2^(4*n^2) * Product[Product[1 - Cos[j*Pi/(2*n+1)]^2 * Cos[k*Pi/(2*n+1)]^2, {j, 1, n}], {k, 1, n}], {n, 0, 10}] // Round (* Vaclav Kotesovec, Jan 03 2021 *)

PROG

(PARI) default(realprecision, 120);

{a(n) = round(4^(2*n^2)*prod(j=1, n, prod(k=1, n, 1-(cos(j*Pi/(2*n+1))*cos(k*Pi/(2*n+1)))^2)))}

CROSSREFS

Cf. A093967, A340166, A340185, A340292, A340295.

Sequence in context: A068939 A179106 A157643 * A104682 A185902 A013756

Adjacent sequences:  A340288 A340289 A340290 * A340292 A340293 A340294

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jan 03 2021

STATUS

approved

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Last modified May 12 22:36 EDT 2021. Contains 343829 sequences. (Running on oeis4.)