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A127605
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a(n) = 2^(2*n*n) * Product_{i=1..n} Product_{j=1..n} (sin(i*Pi/(2*n+1))^2 + sin(j*Pi/(2*n+1))^2).
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7
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1, 6, 500, 463736, 4614756624, 485005220494432, 533978739649683515200, 6129678550595328659594928000, 731483813983605533022316212534132992, 905665520470954445892575061753881157482726912
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ Gamma(1/4) * exp(G*(2*n+1)^2/Pi) / (2^(3/2) * Pi^(3/4) * sqrt(n)), where G is Catalan's constant A006752. - Vaclav Kotesovec, Dec 30 2020
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MAPLE
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for n from 0 to 12 do a[n]:=2^(2*n*n)*product(product(sin(i*Pi/(2*n+1))^2+ sin(j*Pi/(2*n+1))^2, j=1..n), i=1..n) od: seq(round(evalf(a[n], 300)), n=0..12);
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MATHEMATICA
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Table[(2*n+1) * 2^(n*(2*n-1)) * Product[Product[Sin[i*Pi/(2*n + 1)]^2 + Sin[j*Pi/(2*n + 1)]^2, {i, 1, j-1}], {j, 2, n}]^2, {n, 0, 15}] // Round (* Vaclav Kotesovec, Dec 30 2020 *)
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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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