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A340166
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a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 - sin(i*Pi/(2*n))^2 * sin(j*Pi/(2*n))^2).
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10
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1, 12, 17745, 2958176256, 54090331699622625, 107181043200192494332800000, 22868509031094388112997259982567521313, 523389340935243821042846225254323436248483571433472
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 - cos(i*Pi/(2*n))^2 * cos(j*Pi/(2*n))^2).
a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 - sin(i*Pi/(2*n))^2 * cos(j*Pi/(2*n))^2).
a(n) ~ Gamma(1/4) * exp(8*G*n^2/Pi) / (Pi^(3/4) * sqrt(n) * 2^(6*n - 2)), where G is Catalan's constant A006752. - Vaclav Kotesovec, Jan 05 2021
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MATHEMATICA
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Table[4^(2*(n-1)^2) * Product[Product[1 - Sin[i*Pi/(2*n)]^2 * Sin[j*Pi/(2*n)]^2, {i, 1, n-1}], {j, 1, n-1}], {n, 1, 10}] // Round (* Vaclav Kotesovec, Dec 31 2020 *)
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PROG
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(PARI) default(realprecision, 120);
{a(n) = round(4^(2*(n-1)^2)*prod(i=1, n-1, prod(j=1, n-1, 1-(sin(i*Pi/(2*n))*sin(j*Pi/(2*n)))^2)))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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