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A340293
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a(n) = 4^((n-1)*n) * Product_{1<=j<k<=n} (1 - sin(j*Pi/(2*n+1))^2 * sin(k*Pi/(2*n+1))^2).
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2
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1, 1, 11, 1247, 1455913, 17511093953, 2169916151129091, 2770393222231417622719, 36443188794328204864735075793, 4939371777650229260975457785579794433, 6897784079863728378183626237683602071537213179
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ exp(G*(2*n+1)^2/Pi) / (2^(2*n - 1/8) * (1 + sqrt(2))^(n + 1/2)), where G is Catalan's constant A006752. - Vaclav Kotesovec, Jan 04 2021
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MATHEMATICA
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Table[2^(2*n*(n-1)) * Product[Product[1 - Sin[j*Pi/(2*n + 1)]^2*Sin[k*Pi/(2*n + 1)]^2, {k, j+1, n}], {j, 1, n}], {n, 0, 12}] // Round (* Vaclav Kotesovec, Jan 04 2021 *)
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PROG
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(PARI) default(realprecision, 120);
{a(n) = round(4^((n-1)*n)*prod(j=1, n, prod(k=j+1, n, 1-(sin(j*Pi/(2*n+1))*sin(k*Pi/(2*n+1)))^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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